Question

The set of values of k for which the given quadratic equation has real roots
$2x^2+kx+4=0$ is $k$ $\ge 4\sqrt{2}$ and $k\le -4\sqrt{2}$

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ The given quadratic equation is $2x^2+kx+4=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We get, $a=2,b=k,c=4$

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

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

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

$\Rightarrow$ $k^2-32\ge 0$

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

$\Rightarrow$ $k\le -4\sqrt{2}$ or $k\ge 4\sqrt{2}$