Worksheets Chapter 2 Polynomials Class 10 Mathematics

Students should refer to Worksheets Class 10 Mathematics Polynomials Chapter 2 provided below with important questions and answers. These important questions with solutions for Chapter 2 Polynomials have been prepared by expert teachers for Class 10 Mathematics based on the expected pattern of questions in the Class 10 exams. We have provided Worksheets for Class 10 Mathematics for all chapters on our website. You should carefully learn all the important examinations questions provided below as they will help you to get better marks in your class tests and exams.

Polynomials Worksheets Class 10 Mathematics

VERY SHORT ANSWER TYPE QUESTIONS

Question. What will be the number of zeros of a linear polynomial p(x) if its graph (i) passes through the origin. (ii) doesn’t intersect or touch x-axis at any point?
Ans. (i) 1 (ii) 0

Question. If α and 1/α are zeros of 4x² – 17x + k – 4, find the value of k.
Ans. k = 8

Question. If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and – 3, then
(a) a = – 7, b = – 1
(b) a = 5, b = – 1
(c) a = 2, b = – 6
(d) a = 0, b = – 6
Ans. (d) a = 0, b = –6

Question. What will be the number of real zeros of the polynomial x² + 1?
Ans. 0

Question. What should be added to the polynomial x² – 5x + 4, so that 3 is the zero of the resulting polynomial:
(a) 1
(b) 2
(c) 4
(d) 5
Ans. (b) 2

Question. If one zero of the polynomial P(x) = 5x² + 13x + K is reciprocal of the other, then value of k is
(a) 0
(b) 5
(c) 1/6
(d) 6
Ans. (b) 5

Question. If α and β are the zeros of the polynomial
ƒ(x) = x² + x + 1, then 1/α + 1/β =
Ans. – 1

Question. What will be the number of zeros of the polynomials whose graphs are parallel to (i) y-axis (ii) x-axis?
Ans. (i) 1 (ii) 0

Question. If a quadratic polynomial ƒ(x) is not factorizable into linear factors, then it has no real zero. (True/False)
Ans. True

Question. If a quadratic polynomial ƒ(x) is a square of a linear polynomial, then its two zeros are coincident. (True/False).
Ans. True

SHORT ANSWER TYPE (I) QUESTIONS

Question. If α and β are zeros of the polynomial t² – t – 4, form a quadratic polynomial whose zeros are 1/α and 1/β .
Ans. 4t² + t – 1

Question. If zeros of x² – kx + 6 are in the ratio 3 : 2, find k.
Ans. – 5, 5

Question. For what value of k, x² – 4x + k touches x-axis.
Ans. 4

Question. If one zero of the quadratic polynomial (k² + k)x² + 68x + 6k is reciprocal of the other, find k.
Ans. 5

Question. Find a quadratic polynomial whose zeros are (3+√5)/5 and (3-√5)/5.
Ans. α + β = 6/5, αβ = 4/25, 25x² – 30x + 4

SHORT ANSWER TYPE (II) QUESTIONS

Question. If x⁴ + 2x³ + 8x² + 12x + 18 is divided by (x² + 5) , remainder comes out to be (px + q) , find values of p and q.
Ans. p = 2, q = 3

Question. If zeros of the polynomial ax² + bx – c, a ≠ 0 are additive inverse of each other then what is the value of b?
Ans. b = 0

Question. –5 is one of the zeros of 2x² + px – 15, zeroes of p(x² + x) + k are equal to each other. Find the value of k.
Ans. 7/4

Question. Obtain zeros of 4√3x² + 5x – 2√3 and verify relation between its zeroes and coefficients.
Ans. -2/√3, √3/4

Question. Find the value of k such that 3x² + 2kx + x – k – 5 has the sum of zeros as half of their product.
Ans. 1

LONG ANSWER TYPE QUESTIONS

Question. If (x + 2) is a factor of x² + px + 2q and p + q = 4 then what are the values of p and q?
Ans. p = 4, q = 0

Question. If two zeros of x⁴ – 6x³ – 26x² + 138 x – 35 are (2±√3), find other zeroes.
Ans. – 5, 7

Question. Form a quadratic polynomial one of whose zero is 2 + √5 and sum of the zeros is 4.
Ans. 2-√5

Question. Obtain all zeros of the polynomial 2x⁴ – 2x³ – 7x² + 3x + 6 if two factors of this polynomial are (x±√3/2).
Ans. 2, -1, ±√3/2

Question. Find all zeros of the polynomial 2x³ + x² – 6x – 3 if two of its zeroes are √3 and – √3.
Ans. √3, – √3, -(1/2)

Question. If sum of the zeros of 5x² + (p + q + r)x + pqr is zero, then find p³ + q³ + r³.
Ans. Product of the zeros = 3 pqr

Question. If the polynomial x⁴ – 3x³ – 6x² + kx – 16 is exactly divisible by x² – 3x + 2, then find the value of k.
Ans. x² – 3x + 2 = (x – 2) (x – 1)
P(1) = 0, K = 24.

Question. What should be subtracted from x³ – 3x² + 6x – 15, so that it is completely divisible by (x – 3)?
Ans. 3

Question. If α and β are zeros of the polynomial x² + 4x + 3, find the polynomial whose zeros are 1 + β/α and 1 + α/β
Ans. x² – (16/3)x + 16/3 or 1/3(3x² – 16x + 16)