Question

If one root of $x^2+ax+8=0$ is $4$ and the equation $x^2+ax+b=0$ has equal roots, then $b=$

• A. $7$
• B. $9$
• C. $1$
• D. $3$

Answer 1

Answer: (B)

$9$

$x^2+ax+8=0$ has one of it roots as $4$

$\Rightarrow 4^2+4a+8=0$

$\Rightarrow 4[4+a+2]=0$

$\Rightarrow 6+a=0$

$\Rightarrow a=-6$

Now, the equation

$\Rightarrow x^2+ax+b=0$

$x^2-6x+b=0$

has double ( equal ) roots.

In a quadratic equation, the roots will be equal if and only if the discrimination (D)=0

Now, the discriminant of the above quadratic equation is

$\Rightarrow D=B^2-4AC=0$

$\Rightarrow 6^2-4\cdot 1\cdot b=0$

$\Rightarrow 6^2=4b$

$\Rightarrow b=\frac{36}{4}=9$

$\therefore a=-6$ and $b=9$

Hence, the answer is $9.$