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

A and D

Step-by-step 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

The first choice and the last have no real roots.

Step-by-step 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