Ask Me Help Desk - Discriminant of these questions

The general form of a quadratic equation is $ax^2 + bx + c = 0$

The discriminant is $b^2-4ac$

It comes from the equation:

$x = \frac {-b\,\pm\,\sqrt {b^2-4ac} } {2a}$

1. If it's negative, the roots are complex (not real) because the square root of a negative number is a complex number.

2. If it's zero, the roots are real and equal

3. If it's positive, the roots are real and distinct.

So, for this equation $2x^2 + 2x - 1 = 0$

a = 2, b = 2, c = -1

$b^2-4ac = 2\times2 - 4\times 2 \times -1 = 4 + 8 = 12$

The discriminant is positive, so the roots are real and distinct.

Can you figure out the others now?