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antifrog16 · Oct 13, 2009, 02:16 PM

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

Perito · Oct 13, 2009, 02:33 PM

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?