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  4. If a, b, c ∈ R are such that 4 a+2 b+ c>0 and a x2+b x+ c=0 has no real roots, then the value of (c+ a)(c +b) is

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Q. If $a, b, c \in R$ are such that $4 a+2 b+ c>0$ and $a x^{2}+b x+ c=0$ has no real roots, then the value of $(c+ a)(c +b)$ is

AP EAMCETAP EAMCET 2018

Solution:

Since, the equation $a x^{2}+b x +c=0$
have no real roots and $4 a+2 b+ c>0$
$\therefore a +b +c >0$
$\left\{\because a x^{2}+b x+ c>0, \forall x \in R\right\}$
So, $c+ a>-b$ and $c+b>-a$
$\Rightarrow (c +a)(c +b) >a b$