Please refer to Assignments Class 10 Mathematics Polynomials Chapter 2 with solved questions and answers. We have provided Class 10 Mathematics Assignments for all chapters on our website. These problems and solutions for Chapter 2 Polynomials Class 10 Mathematics have been prepared as per the latest syllabus and books issued for the current academic year. Learn these solved important questions to get more marks in your class tests and examinations.

## Polynomials Assignments Class 10 Mathematics

**VERY SHORT ANSWER TYPE QUESTIONS**

**Question. If one zero of the quadratic polynomial x ^{2} + 3x + k is 2, then the value of k is**

(a) 10

(b) – 10

(c) 5

(d) – 5

**Ans.**(b) –10

**Question. If p(x) = x ^{3} – 2x^{2} – x + 2 = (x + 1) (x – 2) (x – d) then what is the value of d?**

**Ans.**1

**Question. Find the quadratic polynomial whose zeros are**

(5+ 2√3) and (5 – 2√3)**Ans.** x^{2} – 10x + 13

**Question. What will be the number of zeros of the polynomials whose graphs are either touching or intersecting the axis only at the points:**

(i) (–3, 0), (0, 2) & (3, 0)

(ii) (0, 4), (0, 0) and (0, –4)**Ans.** (i) 2 (ii) 1

**Question. What number should be subtracted to the polynomial x ^{2} – 5x + 4, so that 3 is a zero of polynomial so obtained.**

**Ans.**(– 2)

**Question. If α and β are the zeroes of the polynomial p(x) = x ^{2} – p(x + 1) – c such that (α + 1) (β + 1) = 0, the c = _______ .**

**Ans.**1

**Question. How many (i) maximum (ii) minimum number of zeroes can a quadratic polynomial have?****Ans.** (i) 2 (ii) 0

**Question. The quadratic polynomial ax ^{2} + bx + c, a ≠ 0 is represented by this graph then a is**

(a) Natural no.

(b) Whole no.

(c) Negative Integer

(d) Irrational no.**Ans.** (c) Negative Integer

**Question. If α and β are zeros of polynomial 6x ^{2} – 7x – 3, then form a quadratic polynomial where zeros are 2α and 2β**

**Ans.**[3x

^{2}– 7x – 6] k

**Question. If one zero of p(x) = 4x ^{2} – (8k^{2} – 40k) x – 9 is negative of the other, find values of k.**

**Ans.**k = 0, 5

**SHORT ANSWER TYPE (I) QUESTIONS**

**Question. If α and β are the zeros of the polynomial x ^{2} – 5x + m such that α – β = 1, find m.**

**Ans.**6

**Question. If m and n are the zeros of the polynomial 3x ^{2} + 11x – 4, find the value of m/n + n/m.**

**Ans.**m/n + n/m = (m

^{2}+n

^{2})/mn = ((m+n)

^{2}-2mn)/mn = (-(11/3)

^{2}– 2(-4/3))/-(4/3) = 145/12

**Question. If the sum of squares of zeros of the polynomial x ^{2} – 8x + k is 40, find the value of k.**

**Ans.**12

**Question. If the product of zeros of ax ^{2} – 6x – 6 is 4, find the value of a. Hence find the sum of its zeros.**

**Ans.**a = 3/2, sum of zeroes = – 4

**Question. What should be added to the polynomial x ^{3} – 3x^{2} + 6x – 15, so that it is completely divisible by x – 3 ?**

**Ans.**On dividing x

^{3}– 3x

^{2}+ 6x – 15 by x – 3, remainder is + 3, hence – 3 must be added to x

^{3}– 3x

^{2}+ 6x – 15.

**SHORT ANSWER TYPE (II) QUESTIONS**

**Question. If (k+ y) is a factor of each of the polynomials y ^{2} + 2y – 15 and y^{3} + a , find the values of k and a.**

**Ans.**k = –3, 5 and a = –27, 125

**Question. What must be added to 4x ^{4} + 2x^{3} – 2x^{2} + x – 1 so that the resulting polynomial is divisible by x^{2} – 2x – 3 ?**

**Ans.**61x – 65

**Question. If α and β are zeros of x ^{2} – x – 2, find a polynomial whose zeros are (2α+1) and (2β+1)**

**Ans.**x

^{2}– 4x – 5

**Question. What must be subtracted from 8x ^{4} + 14x^{3} – 2x^{2} + 7x – 8 so that the resulting polynomial is exactly divisible by 4x^{2} + 3x – 2 ?**

**Ans.**14x – 10

**Question. Find values of a and b so that x ^{4} + x^{3} + 8x^{2} + ax + b is divisible by x^{2} + 1.**

**Ans.**a = 1, b = 7

**LONG ANSWER TYPE QUESTIONS**

**Question. If the zeros of x ^{2} + px + q are double in value to the zeros of 2x^{2} – 5x – 3 find p and q.**

**Ans.**p = – (5/4) and q = -(3/8)

**Question. Find K, so that x ^{2} + 2x + K is a factor of 2x^{4} + x^{3} – 14x^{2} + 5x + 6. Also find all the zeros of the two polynomials:**

**Ans.**On dividing 2x

^{4}+ x

^{3}– 14x

^{2}+ 5x + 6 by x

^{2}+ 2x + k

We get (7k + 21)x + 2k

^{2}+ 8k + 6 as remainder is zero.

⇒ 7k + 21 = 0 and 2k

^{2}+ 8k + 6 = 0

⇒ k = – 3 and k = –1 or – 3

⇒ k = – 3

quotient = 2x

^{2}– 3x – (2k + 8)

= 2x

^{2}– 3x – 2

Zeros of x

^{2}+ 2x – 3 are 1, – 3 and 2x

^{4}+ x

^{3}– 14x

^{2}+ 5x + 6 are 1, -3, 2, -(1/2)

**Question. If x – √5 is a factor of the cubic polynomial x ^{3} – 3√5x^{2} + 13x – 3√5 , then find all the zeros of the polynomial.**

**Ans.**√5, √5 + √2 , √5 – √2

**Question. If √2 is a zero of (6x ^{3} + √2x^{2} –10x – 4√2) , find its other zeroes.**

**Ans.**-(√2/2), (-2√2)/3

**Question. If zeros of x ^{2} – 5kx + 24 are in the ratio 3 : 2, find k.**

**Ans.**k = 2

**Question. If the polynomial x ^{4} – 6x^{3} + 16x^{2} – 25x + 10 is divided by x^{2} – 2x + k, the reaminder is (x + a) then find the value of k and a.**

**Ans.**On dividing x

^{4}– 6x

^{3}+ 16x

^{2}– 25x + 10 by x

^{2}– 2x + k we get remainder

(2k – 9)x + (10 – 8k + k

^{2})

Given remainder = x + a

2k – 9 = 1 ⇒ k ⇒ 5

10 – 8k + k

^{2}= a ⇒ a = 10 – 40 + 25 = – 5

a = – 5, k = 5

**Question. Form a polynomial whose zeros are the reciprocal of the zeros of p(x) = ax ^{2} + bx + c, a ≠ 0.**

**Ans.**k[x

^{2}+(b/c)x+(a/c)]

**Question. If x ^{2} + 1 is a factor of x^{4} + x^{3} + 8x^{2} + ax + b then what are the values of a and b.**

**Ans.**a = 1, b = 7