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. $11$
• E. $9$

Answer 1

The correct option is C $-11$

Given equation

$2x^2+(a+3)x+8=0$

Here $A=2,B=a+3,C=8$

If roots are equal then

$B^2-4AC=0$

$\Rightarrow {(a+3)}^2-4\times 2\times 8=0$

$\Rightarrow a^2+6a+9-64=0$

$\Rightarrow a^2+6a-55=0$

$\Rightarrow a^2+11a-5a-55=0$

$\Rightarrow (a+11)(a-5)=0$

$\therefore a=-11,5$