Question

The set of values of k for which the given quadratic equation has real roots
$x^2-kx+9=0$ is k $\le$ -6 or k $\ge$ 6

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ The given quadratic equation is $x^2-kx+9=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We have, $a=1,b=-k,c=9$

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

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

$\Rightarrow$ $(-k{)}^2-4(1\left)\right(9)\ge 0$

$\Rightarrow$ $k^2-36\ge 0$

$\Rightarrow$ $k^2-(6{)}^2\ge 0$

$\Rightarrow$ $(k+6)(k-6)\ge 0$

$\Rightarrow$ $k\le -6$ or $k\ge 6$