Question

The values of k for which the given quadratic equation has real and distinct roots
$x^2$ - kx + 9 = 0 is $k<-6$ $or$ $k>6$.

• 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 $a{x}^2+bx+c=0$

$\therefore$ We get, $a=1b=-k,c=9$

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

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

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

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

$\Rightarrow$ $k^2>36$

$\Rightarrow$ $k>6$ or $k<-6$

$\therefore$ We can see values of $k$ given in question are correct.