Question

Use the discriminant to determine the number and type of solutions the equation has.

x2 + 8x + 12 = 0

no real solution
one real solution
two rational solutions
two irrational solutions

Answer 1

You should show your result. What is the Discriminant?

Answer 2

16

Answer 3

\(8^{2} - 4(1)(12) = 64 - 48 = 16\)

Okay, I'll buy it. Now, what does that tell us?

Answer 4

um, well, it tells us that...i have no idea

Answer 5

You'll have to do better than that.

Think about the Quadratic Formula. \(x = \dfrac{-b\pm\sqrt{b^{2} - 4ac}}{2a}\)

The stuff under the radical is the "Discriminant". What does it discriminate?

Q1) What happens if Discriminant < 0?? What happens to the radical when the value is NEGATIVE?

Answer 6

If the discriminant is <0 there are two unequal complex roots? If the discriminant is negative, there are two conjugate complex solutions. Sorry.

Answer 7

Okay, now let's think about the possible answers from which we are allowed to choose. We are talking about Real Numbers only.

So, if we are talking about ONLY the Real Numbers, if Discriminant < 0, there are NO Real Solutions. Do you agree?

Answer 8

Yes, so that would be the first one or is there more to consider?

Answer 9

Your discriminant was +16. Since \(Discriminant \ge 0\), there is at least one Real Solution.