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