Question

The set of values of k for which the given quadratic equation has real roots
$2x^2$ + 3x + k = 0 are k $\le \frac{9}{8}$

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ The given equation is $2x^2+3x+k=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We have, $a=2,b=3,c=k$

$\Rightarrow$ It is given that roots are real.

$\therefore$ $b^2-4ac\ge 0$

$\Rightarrow$ $(3{)}^2-4(2\left)\right(k)\ge 0$

$\Rightarrow$ $9-8k\ge 0$

$\Rightarrow$ $8k\le 9$

$\therefore$ $k\le \frac{9}{8}$

$\Rightarrow$ Hence, we can see given value of $k$ is correct.