Question

If $y={\log }_{(7-a)}(2x^2+2x+a+3)$ is defined for all $x\in R,$ then possible integral value(s) of $a$ is (are)

• A. $-3$
• B. $-2$
• C. $4$
• D. $5$

Answer 1

Answer: (B), (C), (D)

$5$

$7-a>0\Rightarrow a<7,$
$7-a\ne 1\Rightarrow a\ne 6$

$2x^2+2x+a+3>0\forall x\in R$
$\Rightarrow D<0$
$\Rightarrow 4-4\cdot 2(a+3)<0$
$\Rightarrow 1-2a-6<0$
$\Rightarrow a>-\frac{5}{2}$
$\Rightarrow a\in (-\frac{5}{2},6)\cup (6,7)$