If-R-are-the-roots-of-the-equation-ax-2-bx-c-0-k-R-lies-between-and-if-

Question Number 5206 by ´[ last updated on 30/Apr/16

If α, β \in R, are the roots of the equation

{a x}^{2} + b x + c = 0, k \in R lies between α and

β, if

Commented by prakash jain last updated on 30/Apr/16

{a x}^{2} + b x + c takes a sign opposite of a for α < k < β

\Rightarrow {a k}^{2} + b k + c has the sign - a

\Rightarrow a^{2} k^{2} + a b k + a c < 0