Question

Give zeroes of quadradic polynomial x² + 2x– 15.

(A) 3 and 5

(B) –3 and –5

(C) 3 and –5

(D) –3 and 5​

Answer 1

Question:-

$\sf{To\: find \:the \:zeroes\: of \:the\: polynomial = x^2 + 2x - 15}$

Solution:-

$\sf{p(x) = x^2 + 2x - 15 = 0}$

= $\sf{x^2 + 5x - 3x - 15 = 0}$

= $\sf{x(x + 5) - 3(x + 5) = 0}$

= $\sf{(x+5)(x-3) = 0}$

Either,

$\sf{x + 5 = 0}$

=> $\sf{x = -5}$

Or,

$\sf{x - 3 = 0}$

=> $\sf{x = 3}$

$\sf{\therefore The\:zeroes\:of\:the\:polynomial\:x^2+2x-15\:are\:3\:and\:-5}$

Verification:-

$\sf{Sum\:of\:zeroes = \dfrac{-Coefficient\:of\:x}{Coefficient\:of\:x^2}}$

= $\sf{3 + (-5) = \dfrac{-2}{1}}$

= $\sf{-2 = -2 \:\:\:[Verified]}$

$\sf{Product\:of\:zeroes = \dfrac{Constant\:term}{Coefficient\:of\:x^2}}$

= $\sf{3\times -5 = \dfrac{-15}{1}}$

= $\sf{-15 = -15 [Verified]}$

$\sf{\therefore Option(C)\: is\:the\:correct\:answer}$