If the equation x^4 - 4X^3 + ax^2 + bx + 1 = 0 has four...

[MoniqueK]

If the equation x^4 - 4X^3 + ax^2 + bx + 1 = 0 has four positive roots, then the values of a & b are?

Can anyone help? The explanation that I have does not make any sense to me.

Thank you in advance!

[Stuart@KaplanGMAT]

If the equation x^4 - 4X^3 + ax^2 + bx + 1 = 0 has four positive roots, then the values of a & b are?

Can anyone help? The explanation that I have does not make any sense to me.

Thank you in advance!

Where is this question from? The level of algebra is way beyond anything I've seen on the GMAT before. You're not expected to be able to solve quardics (and certainly don't need to know the quardic equation formula).

The only reasonably efficient (and still ugly) way I can think of to answer this is to backsolve, which we can't do without any answer choices.

[MoniqueK]

It's actually a question from material obtained through 4gmat.com. I had exhausted the OG Books and still was scoring in the 650 range, so it was suggested by another member of this forum to try those books out. I definitely agree that the material is on the tougher side, but I have gotten something out of it.

I continuously score higher on the verbal portion of the exam as opposed to the math. I have discovered that timing is my main issue as I struggle with the idea of guessing on problems and always run out of time on the official exam.

Please let me know if you have other suggestions. I am hitting crunch time as my exam is on the 16th of this month.