Question

$If{x}^2+2ax+a<0forallxϵ[1,2]then:$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$f\left(x\right)=x^2+2ax+a<0\forall xϵ[1,2]$

$\Rightarrow$ f(1) < 0 , f(2) < 0, D $\ge$ 0

$\Rightarrow$ 3a + 1 < 0 , 5a +4 < 0 , a(a-1) $\ge$ 0

$\Rightarrow$ a < $\frac{-1}{3}$, a <$\frac{-4}{5}$,$a\le 0ora\ge 1$

$\Rightarrow$ - $\infty$ < a < - $\frac{4}{5}$ i.e., a $ϵ$ $(-\infty ,-\frac{4}{5})$ .