Question

If the equation $2x^2 - (a+3)x + 8 = 0$ has equal roots, then one of the values of $a$ is

• A. -9
• B. -5
• C. -11
• D. 11

Answer 1

Answer: (C)

-11

Answer 2

Given equation is $2 x^{2}+(a+3) x+8=0$
Here, $A=2, B=a+3$ and $C=8$
If roots are equal, then $B^{2}-4 A C=0$
$\Rightarrow (a+3)^{2}-4 \times 2 \times 8=0$
$\Rightarrow a^{2}+6 a+9-64=0$
$\Rightarrow a^{2}+6 a-55=0$
$\Rightarrow a^{2}+11 a-5 a-55=0$
$\Rightarrow (a+11)(a-5)=0$
$\therefore a=-11,5$