Question

Which quadratic equation has no real roots?

Choose exactly two answers that are correct.





–x2 + 2x – 6 = 0



–2x2 + 3x + 4 = 0



2x2 + x – 6 = 0



2x2 – x + 3 = 0

Answer 1

The first choice and the last have no real roots.

Explanation:

For an equation to have no real roots the value of the discriminant ( b^2 - 4ac) will be negative.

Working out the values:

1. D = (-2)^2 - 4* -1*-6 = -20 so it has no real roots.

2. D = (3)^2 - 4* -2* 4 = 41 so it does have real roots.

3. D = (1)^2 - 4* 2*-6 = 49 so real roots.

4. D = (-1)^2 - 4* 2*3 = -23 so no real roots

Answer 2

A and D

Explanation:

By finding the roots of all the equations, we see that options A and D are the only ones that require an imaginary number in order to solve