Question

The value of k for which the roots are real and equal of the following equation $9x^2$ - 24x + k = 0 is $k=16$

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ The given quadratic equation is $9x^2-24x+k=0$, comparing it with $a{x}^2+bx+c=0$ we get,

$\Rightarrow$ $a=9,b=-24,c=k$

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

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

$\Rightarrow$ $(-24{)}^2-4(9\left)\right(k)=0$

$\Rightarrow$ $576-36k=0$

$\Rightarrow$ $36k=576$

$\therefore$ $k=16$

$\therefore$ The given statement is true.