Question

Which of the following quadratic equation have equal roots?

• A. $x^2-6x+4=0$
• B. $x^2-8x-16=0$
• C. $x^2-8x+16=0$
• D. $2x^2-2x+4=0$

Answer 1

The correct option is C $x^2-8x+16=0$

A quadratic equation will have equal roots if its discriminant value is 0.
i.e D = $b^2-4ac$ = 0.

For $x^2-6x+4=0$,
D = $(-6{)}^2-4(1\left)\right(4)$ = 20
So, the quadratic equation
$x^2-6x+4=0$ does not have equal roots.

For $x^2-8x-16=0$,
D = $(-6{)}^2-4(1\left)\right(-16)$ = 128
So, the quadratic equation
$x^2-8x-16=0$ does not have equal roots.

For $x^2-8x+16=0$,
D = $(-8{)}^2-4(1\left)\right(16)$ = 0
So, the quadratic equation
$x^2-8x+16=0$ have equal roots.

For $2x^2-2x+4=0$,
D = $(-2{)}^2-4(2\left)\right(4)$ = -28
So, the quadratic equation
$x^2-6x+4=0$ does not have equal roots.

$\therefore$ the quadratic equation
$x^2-8x+16=0$ have equal roots.