# Assignments Class 10 Mathematics Polynomials

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 x2 + 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) = x3 – 2x2 – 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. x2 – 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 x2 – 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) = x2 – 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 ax2 + 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 6x2 – 7x – 3, then form a quadratic polynomial where zeros are 2α and 2β
Ans. [3x2 – 7x – 6] k

Question. If one zero of p(x) = 4x2 – (8k2 – 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 x2 – 5x + m such that α – β = 1, find m.
Ans. 6

Question. If m and n are the zeros of the polynomial 3x2 + 11x – 4, find the value of m/n + n/m.
Ans. m/n + n/m = (m2+n2)/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 x2 – 8x + k is 40, find the value of k.
Ans. 12

Question. If the product of zeros of ax2 – 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 x3 – 3x2 + 6x – 15, so that it is completely divisible by x – 3 ?
Ans. On dividing x3 – 3x2 + 6x – 15 by x – 3, remainder is + 3, hence – 3 must be added to x3 – 3x2 + 6x – 15.

SHORT ANSWER TYPE (II) QUESTIONS

Question. If (k+ y) is a factor of each of the polynomials y2 + 2y – 15 and y3 + a , find the values of k and a.
Ans. k = –3, 5 and a = –27, 125

Question. What must be added to 4x4 + 2x3 – 2x2 + x – 1 so that the resulting polynomial is divisible by x2 – 2x – 3 ?
Ans. 61x – 65

Question. If α and β are zeros of x2 – x – 2, find a polynomial whose zeros are (2α+1) and (2β+1)
Ans. x2 – 4x – 5

Question. What must be subtracted from 8x4 + 14x3 – 2x2 + 7x – 8 so that the resulting polynomial is exactly divisible by 4x2 + 3x – 2 ?
Ans. 14x – 10

Question. Find values of a and b so that x4 + x3 + 8x2 + ax + b is divisible by x2 + 1.
Ans. a = 1, b = 7

LONG ANSWER TYPE QUESTIONS

Question. If the zeros of x2 + px + q are double in value to the zeros of 2x2 – 5x – 3 find p and q.
Ans. p = – (5/4) and q = -(3/8)

Question. Find K, so that x2 + 2x + K is a factor of 2x4 + x3 – 14x2 + 5x + 6. Also find all the zeros of the two polynomials:
Ans. On dividing 2x4 + x3 – 14x2 + 5x + 6 by x2 + 2x + k
We get (7k + 21)x + 2k2 + 8k + 6 as remainder is zero.
⇒ 7k + 21 = 0 and 2k2 + 8k + 6 = 0
⇒ k = – 3 and k = –1 or – 3
⇒ k = – 3
quotient = 2x2 – 3x – (2k + 8)
= 2x2 – 3x – 2
Zeros of x2 + 2x – 3 are 1, – 3 and 2x4 + x3 – 14x2 + 5x + 6 are 1, -3, 2, -(1/2)

Question. If x – √5 is a factor of the cubic polynomial x3 – 3√5x2 + 13x – 3√5 , then find all the zeros of the polynomial.
Ans. √5, √5 + √2 , √5 – √2

Question. If √2 is a zero of (6x3 + √2x2 –10x – 4√2) , find its other zeroes.
Ans. -(√2/2), (-2√2)/3

Question. If zeros of x2 – 5kx + 24 are in the ratio 3 : 2, find k.
Ans. k = 2

Question. If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by x2 – 2x + k, the reaminder is (x + a) then find the value of k and a.
Ans. On dividing x4 – 6x3 + 16x2 – 25x + 10 by x2 – 2x + k we get remainder
(2k – 9)x + (10 – 8k + k2)
Given remainder = x + a
2k – 9 = 1 ⇒ k ⇒ 5
10 – 8k + k2 = 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) = ax2 + bx + c, a ≠ 0.
Ans. k[x2+(b/c)x+(a/c)]

Question. If x2 + 1 is a factor of x4 + x3 + 8x2 + ax + b then what are the values of a and b.
Ans. a = 1, b = 7