Question

Value of k for which the roots are real and equal of the following equation
$2k{x}^2$ - 40x + 25 = 0 is $k=8$

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ The given quadratic equation is $2k{x}^2-40x+25=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We get, $a=2k,b=-40$ and $c=25.$

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

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

$\Rightarrow$ $(-40{)}^2-4(2k\left)\right(25)=0$

$\Rightarrow$ $1600-200k=0$

$\Rightarrow$ $200k=1600$

$\Rightarrow$ $k=8$

$\Rightarrow$ Hence, we have proved that given statement is true.