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 4x ^{2} – 17x + k – 4, find the value of k.**

**Ans.**k = 8

**Question. If the zeroes of the quadratic polynomial x ^{2} + (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 x ^{2} + 1?**

**Ans.**0

**Question. What should be added to the polynomial x ^{2} – 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) = 5x ^{2} + 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) = x^{2} + 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 t ^{2} – t – 4, form a quadratic polynomial whose zeros are 1/α and 1/β .**

**Ans.**4t

^{2}+ t – 1

**Question. If zeros of x ^{2} – kx + 6 are in the ratio 3 : 2, find k.**

**Ans.**– 5, 5

**Question. For what value of k, x ^{2} – 4x + k touches x-axis.**

**Ans.**4

**Question. If one zero of the quadratic polynomial (k ^{2} + k)x^{2} + 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, 25x^{2} – 30x + 4

**SHORT ANSWER TYPE (II) QUESTIONS**

**Question. If x ^{4} + 2x^{3} + 8x^{2} + 12x + 18 is divided by (x^{2} + 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 ax ^{2} + 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 2x ^{2} + px – 15, zeroes of p(x^{2} + x) + k are equal to each other. Find the value of k.**

**Ans.**7/4

**Question. Obtain zeros of 4√3x ^{2} + 5x – 2√3 and verify relation between its zeroes and coefficients.**

**Ans.**-2/√3, √3/4

**Question. Find the value of k such that 3x ^{2} + 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 x ^{2} + 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 x ^{4} – 6x^{3} – 26x^{2} + 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 2x ^{4} – 2x^{3} – 7x^{2} + 3x + 6 if two factors of this polynomial are (x±√3/2).**

**Ans.**2, -1, ±√3/2

**Question. Find all zeros of the polynomial 2x ^{3} + x^{2} – 6x – 3 if two of its zeroes are √3 and – √3.**

**Ans.**√3, – √3, -(1/2)

**Question. If sum of the zeros of 5x ^{2} + (p + q + r)x + pqr is zero, then find p^{3} + q^{3} + r^{3}.**

**Ans.**Product of the zeros = 3 pqr

**Question. If the polynomial x ^{4} – 3x^{3} – 6x^{2} + kx – 16 is exactly divisible by x^{2} – 3x + 2, then find the value of k.**

**Ans.**x

^{2}– 3x + 2 = (x – 2) (x – 1)

P(1) = 0, K = 24.

**Question. What should be subtracted from x ^{3} – 3x^{2} + 6x – 15, so that it is completely divisible by (x – 3)?**

**Ans.**3

**Question. If α and β are zeros of the polynomial x ^{2} + 4x + 3, find the polynomial whose zeros are 1 + β/α and 1 + α/β**

**Ans.**x

^{2}– (16/3)x + 16/3 or 1/3(3x

^{2}– 16x + 16)