Question

If the roots of the quadratic equation $5x^2-2kx+20=0$ are real and equal then the value of $k$ is ________.

• A. $20$
• B. $-10$
• C. $10$ or $-10$
• D. $10$

Answer 1

Answer: (C)

$10$ or $-10$

Quadratic equation:
$5x^2-2kx+20=0$

It is given that the roots of the quadratic equation are real and equal, Then discriminant $D=0$.

Comparing the given equation with $a{x}^2+bx+c=0$

we have $a=5,b=-2k$ and $c=20$

Now, $D=0$

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

$\therefore (-2k{)}^2-4(5\left)\right(20)=0$

$\therefore 4k^2-400=0$

$\therefore k^2=100$

$\therefore k=\pm 10$

Thus, $k=10$ or $-10$.