Question

5x2 – 6x – 9 = 0
Determine the discriminant for the equation.
State the number of solutions.
PLEASE HELP ME!!!

Answer 1

Hey Rachel :)
Recall that for a quadratic in standard form: \(\large\rm ax^2+bx+c=0\)
Solutions are given by,\[\large\rm x=\frac{-b\pm\sqrt{\color{orangered}{b^2-4ac}}}{2a}\]This orange portion, under the root, is what we call the discriminant.

Answer 2

If it turns out that the discriminant is negative,
\(\large\rm \sqrt{\color{orangered}{-\text{#}}}\quad=\quad\sqrt{\text#}~i\)
Then we end up with imaginary portion in our answer.
So that corresponds to complex roots :)

Answer 3

We really only care about the `sign` of the discriminant.

Answer 4

a=5
b=-6
c=-9

Plug in the values, what do you get? :)
b^2 - 4ac

Answer 5

Thanks zepdrix,

I don't recall ever knowing that and now that I do, I can go to bed, since I learned something new today.

Answer 6

Oh, and I guess since they're asking for "number of solutions",
they're talking about "real solutions" here.

So ignore what I said about complex roots :)

Answer 7

okay so there would be 2 correct?

Answer 8

Plugging in our values, it looks like we get...\[\large\rm b^2-4ac\quad=\quad (-6)^2-4(5)(-9)\quad=\quad 216\]Positive discriminant, so that corresponds to two roots,
yes good job!

Answer 9

Awesom!!! :)

Answer 10

Lemme summarize that just in case you have more problems like this:

If Discriminant = -# (no solutions)
If Discriminant = 0 (one solution)
If Discriminant = +# (two solutions)