need help on algebra i need some examples on ch.9.6 application of the discriminant finding value of c?

Question

i need notes

Answer 1

I'm not sure what chapter 9.6 is, but knowing the discriminant helps you predict what your roots will be. If your discriminant c is:

c < 0 -- imaginary roots
c = 0 -- double root
c > 0 -- real roots

So for something like x^2 - x - 2 = 0, the discriminant is b^2 - 4ac = (-1)^2 - 4(1)(-2) = 1 + 8 = 9 > 0, so you will end up with real roots. In other words, you can factor it and get a solution for x:

x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x = 2, -1

And these are real roots.

If that had been x^2 - x + 2 = 0, your discriminant would be -7, and you wouldn't be able to factor that. You wouldn't be able to use the quadratic equation either, because you'd end up with a negative under the radical (notice that the discriminant is the same as the expression under the radical).

For something like x^2 + 4x + 4 = 0, your discriminant would be b^2 - 4ac = (4)^2 - 4(1)(4) = 16 - 16 = 0. Factoring, you'd get:

x^2 + 4x + 4 = 0
(x + 2)(x + 2) = 0
x = -2

which turns out to be a double root.

Hopefully this is close to what you're looking for - if not post more on this particular chapter and we'll try to help more.