OpenStudy (anonymous):

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

3 years ago
OpenStudy (tkhunny):

You should show your result. What is the Discriminant?

3 years ago
OpenStudy (anonymous):

16

3 years ago
OpenStudy (tkhunny):

$$8^{2} - 4(1)(12) = 64 - 48 = 16$$ Okay, I'll buy it. Now, what does that tell us?

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (tkhunny):

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?

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (tkhunny):

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?

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (tkhunny):

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

3 years ago