Question

The set of values of k for which the given quadratic equation has real roots
$2x^2+kx+2=0$ is k $\le$ 9

• A. True
• B. False

Answer 1

The correct option is B False

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

$\Rightarrow$ We get, $a=2,b=k,c=2$

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

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

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

$\Rightarrow$ $k^2-16\ge 0$

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

$\Rightarrow$ $(k+4)(k-4)\ge 0$

$\Rightarrow$ $k\ge 4$ and $k\le -4$

$\therefore$ We can see value of $k$ given in question is incorrect.