MCQ Chapter 4 Quadratic Equation Class 10 Mathematics

Please refer to Quadratic Equation MCQ Questions Class 10 Mathematics below. These MCQ questions for Class 10 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Quadratic Equation will help you to prepare for the exams and get more marks.

Quadratic Equation MCQ Questions Class 10 Mathematics

Please see solved MCQ Questions for Quadratic Equation in Class 10 Mathematics. All questions and answers have been prepared by expert faculty of standard 10 based on the latest examination guidelines.

MCQ Questions Class 10 Mathematics Quadratic Equation

Question. If y = 1 is the common root of ly₂ +ly +3=0 and y₂ +y + m = 0, then the value of ‘lm ’ is    
(a) 3
(b) – 4
(c) 4
(d) – 3

Question. Rohan’s mother is 26 years older than him. The product of their ages 3 years from now will be 360, then Rohan’s present age is      
(a) 6 years
(b) 7 years
(c) 10 years
(d) 8 years

Question. If ‘sin α’ and ‘cos α’ are the roots of the equation ax2 + bx + c = 0, then b2 =    
(a) a² + 2ac
(b) a² +ac
(c) a² -ac
(d) a² -2ac

Question. The quadratic equation, sum of whose roots is 3√2 and their product is 5, is    
(a) x² +3√2x -5=0
(b) x² +3√2x +5=0
(c) x² – 3√2x +5=0
(d) x² – 3√2x -5=0

Question. If ax² +bx +c =0 has equal roots, then c is equal to     
(a) b²/2a
(b) b²/4a
(c) -b²/4a
(d) -b²/2a

Question. Which of the following is a quadratic equation?    
(a) x² −x²=(x-1)²
(b) x² +2x +1=(4-x)²+3
(c) -2x²=(5-x)(2x-2/5)
(d) (k+1) x2+3/2x -5 =0,where k = – 1

Question. (x+1)² −x² =0  has    
(a) no real roots
(b) 1 real root
(c) 2 real roots
(d) 4 real roots

Question. 9x² + 12x + 4 = 0 have      
(a) Real and Distinct roots
(b) No real roots
(c) Distinct roots
(d) Real and Equal roots

Question. If the equation (a² +b²)x² −2(ac+bd)x +c²+d2=0  has equal roots, then    
(a) ad=bc
(b) ab=cd
(c) ad=√bc
(d) ab=√cd  

Question. Find the value of ‘p’ for which m = 1/√3 is a root of the equation pm² + (√3 – √2)m-1= 0   
(a) √3
(b) √2
(c) √6
(d) √7

Question. Find the present age of a boy whose age 12 years from now will be the square of his present age.   
(a) 5 years
(b) 7 years
(c) 4 years
(d) 6 years

Question. Which of the following statements is true?     
(a) x² + x + 1 = 0 has no real roots.
(b) x² – 4x +3 = 0 and x² – x – 2 = 0 have two common roots.
(c) x² – 3x – 4 = 0 have real and equal roots.
(d) The roots of ax² + bx + c = 0,a ≠ 0 are reciprocal to each other if a ≠ c .

Question. The length and breadth of a rectangle are (3k + 1) cm and (2k – 1) cm respectively. Find the perimeter of the rectangle if its area is 144cm² .   
(a) 50 cm
(b) 10 cm
(c) 32 cm
(d) 25 cm

Question. What is the nature of the roots of the quadratic equation 25x² – 49 = 0 ?   
(a) Real and distinct
(b) Real and equal
(c) Irrational
(d) No real roots

Question. Divide 63 into two parts such that their product is 962.   
(a) 24, 3C
(b) 28, 35
(c) 26, 37
(d) 27, 36

Question. A quadratic equation αx² +5x +β two roots x = 1/3 and x = -2 . Find the respective values of α and β .   
(a) 3, 2
(b) 2, -5
(c)-3, 5
(d) 3, -2

Question. If a and P are the roots of the equation x² + kx +12 = 0 such that α – β =1 , what is the value of ‘k’?   
(a) 0
(b) ± 5
(c) ±1
(d) ± 7

Question. Which of the following equations has 2 as a root?     
(a) 2x² – 7x + 6 = 0
(b) x² – 4x + 5 = 0
(c) 3x² – 6x – 2 = 0
(d) x² + 3x -12 = 0

Question. If the roots of x² + 4mx + 4m² + m+1= 0 are real, which of the following is true?     
(a) m= -1
(b) m ≤ -1
(c) m ≥ -1
(d) m ≥ 0

Question. What is the value of ‘k’ for which 2x² + kx + k has equal roots?     
(a) 4 only
(b) 0 only
(c) 8 only
(d) 0, 8

Question. Find two consecutive even numbers whose product is double that of the greater number.   
(a) 1, 3
(b) 4, 6
(c) 2, 4
(d) 6, 8

Question. What are the roots of 17a² – 20a + 10 = 10a² + 2a + 7 ?   
(a) 1/7 , 3
(b) 3 , -1/7
(c) -1/7 , 3
(d) -3 , – 1/7

Question. Identify the quadratic equation from the following.     
(a) P + 1/P = 1 , P ≠0
(b) P² + 1/P = 1 , P ≠ 0
(c) x² – 1/x = 1, x ≠ 0
(d) x² + 2√x – 1 = 0

Question. For what respective values of ‘m’ and ‘n’ are  x = -2/5 and x = 5/3 the roots of mx2 + nx – 10 = 0 ?   
(a) 15,-19
(b) -19, 15
(c) 19,-15
(d) -15, 19

Question. Find the roots of the quadratic equation     
(a) -1/2 , 1
(b) -1 , 1/2
(c) 1/2 , 1
(d) -1 , -1/2

Question. The sides of two square plots are (2x -1)m and (5x + 4)m . The area of the second square plot is 9 times the area of the first square plot. Find the side of the larger plot.   
(a) 15m
(b) 13m
(c) 31 m
(d) 39m

Question. Identify the factors of 4x²/5 = 4x – 5 .   
(a) 2/5 , 2/5
(b) -5/2 , 5/2
(c) 5/2 , 5/2
(d) -2/5 , 2/5

Question. The age of a man is the square of his son’s age. A year ago, the man’s age was eight times the age of his son. What is the present age of the man?     
(a) 47 years
(b) 49 years
(c) 36 years
(d) 48 years

Question. Which of the following statements is correct?     
(a) x =1is a root of 2x² + 3x + 1= 0 .
(b) x = 2 is not a root of 6x² + 7x – 5 = 0 .
(c) x = -1is a root of 3x² – x – 1= 0 .
(d) x = – 2/5 is not a root of 5x² – 8x – 4 = 0

Question. If α and β are the roots of 2x² -3x -1=0 , then the value of α² +β² is      
(a) 13/2
(b) 13/4
(c) -13/2
(d) -13/4

Question. The ratio of sum and the product of the roots of  7x² −12x +18=0  is  
(a) 2:3
(b) 3:2
(c) 7:18
(d) 7:12

Question. The sum S of first n even natural numbers is given by the relation S = n(n +1). If the sum is 420, then the value of ‘n’ is
(a) 20
(b) 21
(c) 24
(d) 22

Question. The discriminant of the equation (2a + b) x = x² + 2ab is ______    
(a) (2a + b²)
(b) (2a – b)²
(c) (2a + b)²
(d) (2a –b²)

Question. The perimeter of a right triangle is 70cm and its hypotenuse is 29cm. The area of the triangle is
(a) 210 sq.cm
(b) 200 sq.cm
(c) 180 sq.cm
(d) 250 sq.cm

Question. 5x² +8x +4 =2x² +4x +6  is a
(a) quadratic equation
(b) cubic equation
(c) constant
(d) linear equation

Question. x² – 30x + 225 = 0 have
(a) Real roots
(b) No real roots
(c) Real and Equal roots
(d) Real and Distinct roots

Question. If the quadratic equation bx² -2√acx +b =0 has equal roots, then  
(a) b²=-ac
(b) 2b²=ac
(c) b²=ac
(d) b²=2ac

Question. A quadratic equation ax² +bx +c=0 has real and distinct roots, if
(a) b² -4ac > 0
(b) b² -4ac < 0
(c) None of these
(d) b² -4ac =0

Question. 2x² – 3x + 2 = 0 have
(a) Real and Distinct roots
(b) Real and Equal roots
(c) Real roots
(d) No Real roots

Question. 2x² + 5√3 x + 6 = 0 have
(a) Real and equal root
(b) Real roots
(c) No Real roots
(d) Real and Distinct roots

Question. The value(s) of k, for which the roots of the equation 3x² + 2k + 27 = 0 are real and equal are   
(a) k = 9
(b) k = ± 9
(c) k = –9
(d) k = 0

Question. If one root of the equation (k − 1)x² – 10x + 3 = 0 is the reciprocal of the other, then the value of k is     
(a) 1
(b) 2
(c) 3
(d) 4

Question. The values of k for which the quadratic equation (k + 1)x² + 2(k – 1)x + (k – 2) = 0 has equal roots, is:   
(a) k = 2
(b) k = 3
(c) k = 0
(d) None of these

Question. If quadratic equation 3x² – 4x + k = 0 has equal roots, then the value of k   
(a) 1/3
(b) 2/3
(c) 3
(d) 4/3

Question. The value of k, for which the equation 2x² – 10x + k = 0 has real roots is     
(a) k ≤ 25/2
(b) k ≥ 25/2
(c) k = 25/2
(d) k > 25/2

Question. The value(s) of k for which the quadratic equation 2×2 + kx + 2 = 0 has equal roots, is   
(a) 4
(b) ± 4
(c) – 4
(d) 0

Question. If the quadratic equation x² – 2x + k = 0 has equal roots, then value of k is     
(a) 1
(b) 2
(c) 3
(d) 0

Question. For what value of k, the equation 9x² – 24x + k = 0 has equal roots?    
(a) 12
(b) 16
(c) 18
(d) 20

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): The equation 8x² + 3kx + 2 = 0 has equal roots, then the value of k is ± 8/3 .   
Reason (R): The equation ax² + bx + c = 0 has equal roots if D = b² – 4ac = 0.

Question. Assertion (A): The roots of the quadratic equation x² + 2x + 2 = 0 are imaginary.   
Reason (R): If discriminant D = b² – 4ac < 0, then the roots of quadratic equation ax² + bx + c = 0 are imaginary.

Question. A cyclist takes 2 hours less to cover a distance of 200 km, if he increases his speed by 5 km/hr. Then his original speed is
(a) 26 km/hr
(b) 20 km/hr
(c) 24 km/hr
(d) 25 km/hr

Question. If the roots of the equation (a² +b²)x² -2ab (a+c) x +c² +b²=0 are equal, then
(a) b=ac
(b) b² =ac
(c) b =2ac/a+c
(d) 2b =a +c

Question. A quadratic equation ax² +bx +c =0 has non – real roots, if
(a) b² -4ac > 0
(b) b² -4ac =0
(c) b² -4ac < 0
(d) b² -ac =0

Question. The quadratic equation whose roots are is
(a) 6x² +13x -5=0
(b) 6x² +13x +5=0
(c) 6x² -13x +5=0
(d) 6x² -13x -5=0

Question. If one root of the equation 4x² -2x +(λ-4) =0 be the reciprocal of the other, then the value of λ is
(a) 8
(b) 4
(c) – 8
(d) – 4

(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : (2x – 1)2 – 4x² + 5 = 0 is not a quadratic equation.   
Reason : x = 0, 3 are the roots of the equation 2x² – 6x = 0.

Question. Assertion : Sum and product of roots of 2x² – 3x + 5 = 0 are 3/ 2 and 5/ 2 respectively.     
Reason : If α and β are the roots of ax² + bx + c = 0, a ≠ 0, then sum of roots = α + β – b a = and product of roots αβ = c/a .

Question. Assertion : The equation 9x² + 3kx + 4 = 0 has equal roots for k = ± 4.   
Reason : If discriminant ‘D’ of a quadratic equation is equal to zero then the roots of equation are real and equal.

Question. Assertion : 4x² – 12x + 9 = 0 has repeated roots.     
Reason : The quadratic equation ax² + bx + c = 0 have repeated roots if discriminant D > 0.

Question. Assertion : If roots of the equation x² – bx + c = 0 are two consecutive integers, then b² – 4c = 1.   
Reason : If a, b, c are odd integer then the roots of the equation 4abc x² + (b² – 4ac) x – b = 0 are real and distinct.

Question. Assertion : A quadratic equation ax² + bx + c = 0, has two distinct real roots, if b² – 4ac > 0.   
Reason : A quadratic equation can never be solved by using method of completing the squares.

One Word Questions :

Question. What are the nature of roots of the equation (x – 2a) (x – 2b) = 4ab?

Question. Find the solution set of quadratic equation : 5z² – 3z – 2 = 0.

Question. If S = n(n + 1)/2 = 78 , find n.

Question. What is the solution set of quadratic equation 2z² + az – a² = 0?

Question. For what value of p, the equation 4x² + 8x – p = 0 will have equal roots?

Question. There are three consecutive positive integers such that sum of, the square of the first and product of other two, is 29. What are the integers?

Question. The equation x² Kx p 0 have two roots –4 and –5. What is the value of K?

Question. What is the degree of the equation x(x² 3) 5 x³ 9x² 8.

Question. If , are the roots of the quadratic equation x² 2x – 8 0 , then what is the value of ² ² .

Question. Find two values of x which satisfy the quadractic equation x² – 64 = 0.

Question. If x² + 1/x² = 2 , what are the values of x?

Question. What is the value of D in the equation 9×2 +15x + 4 = 0 ?

Question. Divide 25 into two parts such that their product is 150.

Question. Find two consecutive whole numbers, the difference of whose squares is 15.

Question. What is the value of x in x + 3 /x = 4x ?

Question. For what value of p the quadratic equation, x² – 4x+ p = 0 , will have real and distinct roots?

Question. What is the quadratic equation whose one of the roots is 3– √5 ?

Question. What is the quadratic equations whose roots are 3 and 4.

Question. What is the value of x which satisfies the equation √1 + 27/169 = 1+ x/13 ?

Question. Find the value of x which satisfies the equation : x + 4/x = –4; x 0

Question. For what value of k will the equation 5y² – 20y + (k – 1) = 0 have real and equal roots?

Question. What will be the value of discriminant (D) if the given quadraric equation is perfect square?

Question. Determine the value of p for which the given quadratic equation has real roots :
2x² + 3x + p = 0

Question. Solve the quadratic equation : (x – 2)² – 25 = 0.

Question. What are the two roots of 2x² – 7x = 0?