Question

What are the possible rational zeros of f(x) = x4 + 2x3 - 3x2 - 4x + 12

Answer 1

answers:
± 1, ± 2, ± 3, ± 4, ± 6, ± 12
± 1, ± 2, ± 3, ± 4, ± 5, ± 6, ± 7, ± 8, ± 9, ± 10, ± 11, ± 12
1, 2, 3, 4, 6, 12
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Answer 2

the product of the zeros is 12

so you need the factors of 12 as possible rational zeros...

I would say the 1st option as with an even number of negatives

Answer 3

There are no real roots for \[x^4+2 x^3-3 x^2-4 x+12 \]A plot is attached.The following are the four imaginary roots from Mathematica.\[\left\{\frac{1}{2} \left(-1-\sqrt{9-8 i \sqrt{2}}\right),\frac{1}{2} \left(-1+\sqrt{9-8 i \sqrt{2}}\right),\frac{1}{2} \left(-1-\sqrt{9+8 i \sqrt{2}}\right),\frac{1}{2} \left(-1+\sqrt{9+8 i \sqrt{2}}\right)\right\} \]