Question

Which of the following quadratic equation have imaginary roots?

• A. $2x^2-2x-4=0$
• B. $2x^2-2x+4=0$
• C. $x^2-2x+1=0$
• D. $2x^2-8x+2=0$

Answer 1

The correct option is B $2x^2-2x+4=0$

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

For $2x^2-2x-4=0$,
D = $(-2{)}^2-4(2\left)\right(-4)$ = 36
So, the quadratic equation
$2x^2-2x-4=0$ does not have imaginary roots.

For $2x^2-2x+4=0$,
D = $(-2{)}^2-4(2\left)\right(4)$ = -28
So, the quadratic equation
$2x^2-2x-4=0$ have imaginary roots.

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


For $2x^2-8x+2=0$,
D = $(-8{)}^2-4(2\left)\right(2)$ = 48
So, the quadratic equation
$2x^2-2x-4=0$ does not have imaginary roots.

$\therefore$ the quadratic equation
$2x^2-2x+4=0$ have imaginary roots.