confused on this question

[comeoneileen0405]

Look at the two quadratic equations given below and then choose the answer which best describes their solutions.
4P^2 - 13P + 12 = 0
2b^2 - 7b + 4 = 0

I. Each equation has two distinct real solutions.
II. One equation has two distinct real solutions but the other has one repeated real solution.
III. One equation has two distinct real solutions but the other has no real solutions.
IV. One equation has a repeated real solution but the other has no real solutions.
V. Each equation has one repeated real solution.
VI. Neither equation has any real solutions.
VII. none of these


I am a bit confused on which it would be. I was thinking III but V looks good to me too.
- Eileen

 

[soroban]

Hello, comeoneileen0405!

Look at the two quadratic equations given below and then choose the answer which best describes their solutions.
. . . \(\displaystyle 4P^2\,-\,13P\,+\,12\:=\:0\)
. . . \(\displaystyle 2b^2\,-\,7b\,+\,4\:=\:0\)

I am a bit confused on which it would be. . confused? . . . how come?

It's obvious that you should try to solve them.
. . [Or is it? . Are you waiting for Divine Inspiration?]

Okay, enough sarcasm . . . What did you get?

The first one has: .\(\displaystyle P\:=\:\frac{13\,\pm\,\sqrt{-23}}{8}\) . . . no real solutions

The second one has: .\(\displaystyle b\:=\:\frac{7\,\pm\sqrt{17}}{4}\) . . . two distinct real solutions