ACT Prep problem

I've been working on ACT prep today, and this one has given me some trouble. It's been over two years since I've had Algebra and the Trig/Calc since then hasn't required a lot of some of this stuff. I understand that the roots are the x's, but I was wondering if there is a faster technique than just plugging them all into each equation:

"Which of the following equations given in factored form has roots at 1/2, 3/4, i, and -i?"

A. (2x-1)(4x-3)(x^2 +1) = 0

B. (2x-1)(4x-3)(x^2 -1) = 0

C. (2x+1)(4x-3)(x^2 +1) = 0

D. (2x+1)(4x-3)(x^2 -1) = 0

E. (2x+1)(4x+3)(x^2 +1) = 0

Any help is appreciated, thanks.

Quote:

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Originally Posted by bobsanchez

I've been working on ACT prep today, and this one has given me some trouble. It's been over two years since I've had Algebra and the Trig/Calc since then hasn't required a lot of some of this stuff. I understand that the roots are the x's, but I was wondering if there is a faster technique than just plugging them all into each equation:

"Which of the following equations given in factored form has roots at 1/2, 3/4, i, and -i?"

A. (2x-1)(4x-3)(x^2 +1) = 0

B. (2x-1)(4x-3)(x^2 -1) = 0

C. (2x+1)(4x-3)(x^2 +1) = 0

D. (2x+1)(4x-3)(x^2 -1) = 0

E. (2x+1)(4x+3)(x^2 +1) = 0

Any help is appreciated, thanks.

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Well the question gives a lot of roots, and a lot of factors, but you don't need to do them all that's the trick to taking the ACT and to doing a problem like this. Scan the problem and look at the easist roots to factor in, and they'd be (at least for me) 1/2 and 3/4. Try A and if it fails the 1/2, go to C and then the 3/4, and then if that fails it must be E. You only had to plug in three-four numbers, very fast problem.

If you sat there and plugged it in for each and every one then that would take forever, you just have to see if each individual factor equals 0 as they are 0's.

btw i have no idea if E is right lol i was just using logic

Quote:

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Originally Posted by zany

Well the question gives a lot of roots, and a lot of factors, but you don't need to do them all that's the trick to taking the ACT and to doing a problem like this. Scan the problem and look at the easist roots to factor in, and they'd be (at least for me) 1/2 and 3/4. Try A and if it fails the 1/2, go to C and then the 3/4, and then if that fails it must be E. You only had to plug in three-four numbers, very fast problem.

If you sat there and plugged it in for each and every one then that would take forever, you just have to see if each individual factor equals 0 as they are 0's.

btw i have no idea if E is right lol i was just using logic

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Ah, I remember. Well, I eliminated C-E using using 1/2 and 3/4, and then went back to A and B and did that last term. I think it's A.

Thanks!