Year 12s: what will be the first way you research your future options? >>

Quartic Equation Trouble

Hi there, in our class, we've never done any work on cubic equations, never mind quartic and so I have no idea what to do with this: 9x^4 + 8x^2 - 1

Thanks!

Reply 1

Robocop656

Try using a simple substitution. For these a general rule would be to let y = x^2 meaning you can then substitute this into a new equation. See if you can work it out from there :smile:

Reply 2

L'Evil Fish

It's a quadratic in x^2.

Reply 3

queensboy

Convert it into a quadratic, with a substitution like the poster above said.

Then once you get an answer, sub back in and expand.

Reply 4

Bunneh

Ahh, so re write it as 9y^2 +8y -1?

Reply 5

L'Evil Fish

Original post by Bunneh

Ahh, so re write it as 9y^2 +8y -1?

Solve that

Then your y will equal x^2 so you'll have to square root your value for y

Should get 4 values in total

Reply 6

Bunneh

Original post by L'Evil Fish

Solve that

Then your y will equal x^2 so you'll have to square root your value for y

Should get 4 values in total

One of my values is -1, will some answers be imaginary? The solutions for y are -1 and 1/9 so are my answers +1/3, -1/3, i and -i?

Reply 7

L'Evil Fish

Original post by Bunneh

One of my values is -1, will some answers be imaginary? The solutions for y are -1 and 1/9 so are my answers +1/3, -1/3, i and -i?

Indeed

Reply 8

Mr M

Study Forum Helper

Original post by Bunneh

One of my values is -1, will some answers be imaginary? The solutions for y are -1 and 1/9 so are my answers +1/3, -1/3, i and -i?

Yes. You don't need to state the imaginary answers unless this is a Further Maths question.

Reply 9

Bunneh

Original post by L'Evil Fish

Indeed

Thanks so much!

Just checking, is -i acceptable, I haven't done much work on complex numbers so I assumed that there was a negative imaginary spectrum.

Reply 10

Bunneh

Original post by Mr M

Yes. You don't need to state the imaginary answers unless this is a Further Maths question.

I'm helping a friend but I'm taking Further Maths, so when L'Evil Fish said to root the answers, I just assumed i.

Reply 11

L'Evil Fish

Original post by Bunneh

Thanks so much!

Just checking, is -i acceptable, I haven't done much work on complex numbers so I assumed that there was a negative imaginary spectrum.