I'm just checking my homework guys and I'm not used to this site sorry.

5. Use the discriminant to decide whether the roots of each of the following are real and
distinct, real and equal or not real.

(a) 2x^2 + 2x - 1 = 0 (b) 2x^2 + 2x + 1 = 0


(c) x^2 + 2x + 1 = 0 (d) 9x^2 + 14x + 4 = 0

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?