Question

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² - 5x - 3, find the value of p and q.

Answer 1

2x² − 5x − 3 = 0

2x² − 6x + x − 3 = 0

(x − 3)(2x + 1) = 0

x = 3, −21​

Now,

Zeroes of the polynomial x² + px + q are double in values to the zeroes of polynomial 2x² − 5x − 3.

Therefore,

Zeroes of polynomial x² + px + q will be- 6, −1

Therefore,

Sum of roots = −b​/a

6 + (−1) = −p

⇒ p = -5

Product of root = c​/a

6 × −1 = q

⇒ q = −6

Hence the values of p and q are -5 and −6 respectively.

Answer 2

f(x) = 2x² - 5x - 3

let the zeroes the polynomial be α and β, then