CBSE Class 10 Mathematics Polynomials Worksheet Set J

Question. The value of quadratic polynomial f (x) = 2x²– 3x – 2 at x = -2 is ……
Answer: 12

Question. 2x² -3√x + 5 is a polynomial. True or false. Justify
Answer: false

 Question. The sum and product of the zeroes of a quadratic polynomial are – 1/2 and –3 respectively. What is the quadratic polynomial?
Answer: 2x² + x – 6

Question. Find the zeroes of the polynomial f(x) = 4√3x² + 5x – 2√3
Answer: -2/√3,√3/4

Question. Write a polynomial whose zeroes are √2 and -√2
Answer: x² – 1

Question. What is the zeroes of the polynomial ax + b = 0, a ≠ 0
Answer: –b/a

 Question. If the product of zeroes of the polynomial ax² – 6x – 6 is 4, find the value of a.
Answer: -3/2

Question. Find the zeroes of the polynomial x² – 1.
Answer: +1

Questions of 2 Mark

Question. Obtain all the zeroes of the polynomial x² + 7x + 10 and verify the relationship between the zeroes and its coefficients.
Answer: –5, -2

 Question. Divide 3x² – x³ – 3x + 5 by x – 1 – x² and verify the division algorithm
Answer: Q – (x-2), R = 3

Question. If α and β are the zeroes of the polynomial f(x) = x² – px + q such that α² + β².
Answer: p² – 2q

Question. If α and B are the zeroes of the quadratic polynomial f (x) = x² + 2x + 1, then find 1/∞ and 1/β.
Answer: –2

Question. Check whether 2x³ + 1 is a factor of 2x⁵ + 10x⁴ + 6x³ + 2x² + 5x + 1.
Answer: a = 1, b = + 2, Not a factor

Question. If α and β are the zeroes of the polynomial f(x) = x² – 5x + k such that α – β = 1,find the value of k.
Answer: k = 6

 Question. If two zeroes of the polynomial of (x) = x⁴ – 6x³ – 26x² + 138x – 35 are 2 ± √3 find other zeroes.
Answer: 7, -5

Question. Find the polynomial of least degree which should be subtracted from the polynomial x⁴ + 2x³ – 4x² + 6 x -3 so that it is exactly divisible by x² – x + 1
Answer: 2x – 2

Question. Obtain all the zeroes of the polynomial f(x) = 3x⁴ + 6x³ – 2x² – 10x – 5 if two of its zeroes are √5/3 and – √5/3
Answer: –1, -1

Question. If the polynomial f(x) = x⁴ – 6x³ + 16x² – 25x + 10 is divided by another polynomial x² – 2x + k, the remainder comes out to be x + a, find k and a
Answer: k = 5, a = -5