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 and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
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

	$Thank you very much Sir!$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum