Question

Help, please :)
3x^2-5x+6=0
Calculate the discriminant. Based on answer, tell whether the solution will have real or complex roots. If real, are they rational or irrational? If rational, tell whether or not the two solutions are equal.

Answer 1

The discriminant of a quadratic equation is:\[D=\sqrt{b^2-4ac}\]now you replace your numbers,\[D=\sqrt{5^2-4*3*6}=\sqrt{25-72}=\sqrt{-47}\]therefore you will have two complex solutions.

Answer 2

You're a lifesaver!

Answer 3

Well yes that seems to be the title of my problem solving skills XD

Answer 4

hhaha :)

Answer 5

So what if we had sqrt 109?

Answer 6

\[\sqrt{109}\]

Answer 7

Hello?

Answer 8

If you have 109, it means you have two real solutions. But they are irrational, that means they are fractions. And please forgive me, but the discriminant is \[D=b^2-4ac\] it doesnt have the square root sign at all.

Answer 9

No worries. So what would constitute a rational, equal discriminants?

Answer 10

disregard the s on discriminant. I meant to say: So what would constitute a rational, equal discriminant?

Answer 11

The following table shows info,

If D > 0, it means you have two real solutions (irrational most probably)
If D = 0, it means you have only one real solution
If D < 0, it means you have two complex solutions
If D = square, it means you have two rational solutions.

By square I mean anything in the form c^2.

Answer 12

That is so helpful!! So, if I had a discriminant of 49, would that be rational

Answer 13

Yes, because 7^2 is a perfect square = 49.

Answer 14

Awesome!!! That you so much! You've been tons of help!! :)

Answer 15

You're welcome!