Question

For what value of $k$ will the quadratic equation ${2x}^2+3x+k=0$ have real equal roots ?

• A. $\frac{3}{8}$
• B. $\frac{8}{3}$
• C. $\frac{9}{8}$
• D. $\frac{8}{9}$

Answer 1

The correct option is C $\frac{9}{8}$

$2x^2+3x+k=0$
Here, $a=2,b=3,c=k$
We know that a quardratic equation has real and equal roots if $D=0$

$\therefore D=b^2-4ac={\left(3\right)}^2-4\times 2\times k=9-8k$
$\therefore 9-8k=0\Rightarrow -8k=-9$
$\therefore k=\frac{9}{8}$