Question

If the equation $a{x}^2$$+10x+a=0$ has distinct real roots then the possible value of $a$ is:

• A. -6
• B. -5
• C. -4
• D. 6

Answer 1

The correct option is C -4

$a{x}^2+10x+a=0$

Here,

$A=a$

$B=10$

$C=a$

If both roots are real and distinct,

Therefore, $D>0$

$\Rightarrow B^2-4AC>0$

$\Rightarrow {\left(10\right)}^2-4\left(a\right)\left(a\right)>0$

$\Rightarrow 100-4a^2>0$

$\Rightarrow 4a^2<100$

$\Rightarrow a^2<\frac{100}{4}$

$\Rightarrow a<\pm 5$

$\Rightarrow a\in (-5,5)$

Among the given option, only $-4$ lies in the interval $(-5,5)$.

Hence the correct answer is $\left(C\right)-4$.