Chapter 2 – Polynomials

1) The zeros of the quadratic polynomial:

Calculate the value of

Ans – Given,

3) Zeros of the quadratic polynomial 3x² – kx + 14 are in the ratio 7:6. Calculate the value of ‘k’.

Ans – Let the zeros of the quadratic polynomial, 3x² – kx + 14 be 7p and 6p.

4) Sum and product of zeros of a quadratic polynomial are ‘a’ and ‘1/a’. Identify the quadratic polynomial.

Ans – A quadratic polynomial is given by:

The sum of zeros is given as => a
The the product of zeros is given as => 1/a

Thus, the quadratic polynomial is:

5) Identify the zeros of the given polynomial:

Ans – The polynomial can be written as:

6) Find the zeros of the polynomial f(x) = 2x³ – 7x² + 3x + 6 if its two zeros are

Ans – Given the two zeros of the polynomial f(x) = 2x³ – 7x² + 3x + 6 are:

7) Find the value that must be added to 6x⁵ + 5x⁴ + 11x³ – 3x² + x + 5 so that it can be divided by 3x² – 2x + 4

Ans – When we divide 6x⁵ + 5x⁴ + 11x³ – 3x² + x + 5 with 3x² – 2x + 4 we get:

Hence, we need to add 3x² – 2x + 4 to 6x⁵ + 5x⁴ + 11x³ – 3x² + x + 5 so that it is divisible by 3x² – 2x + 4.

8) By Division method check whether the polynomial (t² – 3) is a factor of the polynomial 2t⁴ + 3t³ – 2t² – 9t -12

Ans – To check whether the polynomial (t² – 3) is a factor, we need to divide 2t⁴ + 3t³ – 2t² – 9t -12 by (t² – 3). Thus, we have

=> (t² – 3) is a factor of the polynomial 2t⁴ + 3t³ – 2t² – 9t -12.