If-a-and-b-0-are-the-roots-of-the-equation-x-2-ax-b-0-then-find-the-least-value-of-x-2-ax-b-x-R-

Question Number 20116 by Tinkutara last updated on 22/Aug/17

If a and b (\neq 0) are the roots of the

equation x^{2} + a x + b = 0, then find the

least value of x^{2} + a x + b (x \in R) .

Answered by ajfour last updated on 22/Aug/17

x^{2} + a x + b = 0 o r

x^{2} - (a + b) x + a b = 0

\Rightarrow a b = b; a + b = - a

\Rightarrow a = 1; b = - 2

s o e q u a t i o n i s x^{2} + x - 2 = 0

\Rightarrow l e a s t v a l u e o f y = x^{2} + x - 2

i s l e a s t v a l u e o f y = {(x + \frac{1}{2})}^{2} - \frac{9}{4}

w h i c h i s e q u a l t o - \frac{9}{4} a t x = - \frac{1}{2} .

Commented by Tinkutara last updated on 22/Aug/17

Thank you very much Sir!