Question

If a and b are the non zero distinct roots of x2 + ax + b = 0, then the minimum value of x2 + ax + b is

Answer 1

Heya

Let :
$p(x) = {x}^{2} + ax + b$

∆ p(x) has non-zero distinct roots

$= > p(x) = {x}^{2} +2 \frac{a}{2} x + \frac{ {a}^{2} }{4} + \frac{4b - {a}^{2} }{4}$

$= > p(x) = (x + \frac{a}{2} )^{2} + \frac{4b - {a}^{2} }{4}$

Hence, the minimum value of p(x) at x = ( -a/2 ) is :
$p( \frac{ - a}{2} ) = \frac{4b - {a}^{2} }{4}$