can't figure this one out

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can someone tell me how to solve:

x^4 - 5x^2 - 36 = 0

i've been trying to approach this problem for 25 mins now. :shock:

what method do you use?

 

[Unco]

Let u = x^2, and solve the resulting quadratic for u, and hence solve for x.

 

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what method do you use to solve the quadratic? factoring doesnt work for me, whats the next easiest step?

 

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i've tried completing the square, quad form, factoring, none of them work for me. can someone please tell me how they got the answer. the answer is +/-2i, +/-3.

i just need to know how to get it

 

[Mrspi]

can someone tell me how to solve:

x^4 - 5x^2 - 36 = 0

i've been trying to approach this problem for 25 mins now. :shock:

what method do you use?

This equation can be written as

(x<SUP>2</SUP>)<SUP>2</SUP> - 5 x<SUP>2</SUP> - 36 = 0

It factors easily:
(x<SUP>2</SUP> - 9)(x<SUP>2</SUP> + 4) = 0

Now, set each factor equal to 0 and solve. You should get the solutions indicated in your previous post.

 

[Unco]

i've tried completing the square, quad form, factoring, none of them work for me. can someone please tell me how they got the answer. the answer is +/-2i, +/-3.

i just need to know how to get it

u^2 - 5u - 36 = 0

Two numbers that multiply to give -36 and add to give -5 are: -9 and +4.

So: u^2 - 5u - 36 = (u - 9)(u + 4)

Now you can replace u with x^2 again.