Question

Which quadratic equation has no real roots? Choose exactly two answers that are correct. Question 12 options: –x2 2x – 6 = 0 –2x2 3x 4 = 0 2x2 x – 6 = 0 2x2 – x 3 = 0.

Answer 1

The quadratic equations that have real roots are $-2x^2+3x+4 = 0$ and  $2x^2+x-6 = 0$.

What is the discriminant of a quadratic equation?

The value of a discriminant of a quadratic equation shows how many roots f(x) have. If the value of the discriminant is greater than 0 then the quadratic equation has real and distinct roots and if the value of the discriminant is equal to 0, then the quadratic equation has real and same roots. In case the value of the discriminant is less than zero then the quadratic equation will have no real roots.

In order to know if the quadratic equation has real roots or not, we need to find the discriminant of the given quadratic equations,

A.) $-x^2+2x -6 = 0$

Here, a= -1, b=2 and c=-6

$D = b^2 -4ac$

$D = 4 -24\\D = -20$

As the value of the discriminant is negative it will not have real roots.

B.) $-2x^2+3x+4 = 0$

Here, a= -2, b=3 and c=4

$D = b^2 -4ac$

$D = 9 +32\\D = 41$

As the value of the discriminant is positive it will have real roots.

C.) $2x^2+x-6 = 0$

Here, a=2, b=1 and c=-6

$D = b^2 -4ac$

$D = 1 +48\\D =49$

As the value of the discriminant is positive it will have real roots.

A.) $2x^2 -x+3 = 0$

Here, a=2, b=-1 and c=3

$D = b^2 -4ac$

$D = 1-24\\D = -23$

As the value of the discriminant is negative it will not have real roots.

Learn more about Discriminant:

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