Important Questions for Class 10 Chapter 2 – Polynomials

If you are preparing for your final board exam or any other test, you can use this free set of important questions for CBSE class 10th Math PDF for practice.

Important questions based on NCERT syllabus for Class 10 Chapter 2 - Polynomials:

Question 1: Factorize z^2 + 3√3z − 12 and verify the relationship between zeroes and coefficient
Solution:
Given polynomial is,
z^2 + 3√3z − 12
= z^2 + 4√3z − √3z − 12
=(z + 4√3)(z − √3)
So the zeroes are,
z + 4√3 = 0
⇒ z = −4√3
z − √3 = 0
⇒ z = √3
For verification,
α + β = −4√3 + √3 = −3√3 = −b/a
αβ = −12 = c/a

Question 2: If 9 and -5 are zeroes of x2+(a+5)x−b are then find the value a and b.
Solution:
Given polynomial is,
x^2+(a+5)x−b
⇒ α + β = −b/a
= −(a+5)/1
⇒ −(a+5)/1 = 9−5
a + 5 = −4
⇒ a = −9
Also,
α + β = c/a = −b/1

⇒ −b/1 = 9 × (−5)

⇒ −b = −45

⇒ b = 45

Question 3: Find the remainders when x4−3x3+4x2−x+4 is divided by
a) x+1
b) x − 1/4
Solution:
We know that,
When a polynomial f(x) is divided by (x−a) the remainder is f(a)
[Remainder theorem]

a) When x^4 − 3x^3 + 4x^2 − x + 4 is divided by x + 1
⇒ (x + 1) = 0
⇒ x = −1
∴ f(−1) = 1 + 3 + 4 + 1 + 4 = 13

b) When x^4−3x^3+4x^2−x+4 is divided by x−1/4
⇒ x−1/4 = 0
⇒ x = 1/4

f(14) = 1/256 + (−3/64) + 1/4 − 1/4 + 4 = 1013/256