Question

2x^4 + 5x^3 + 3x^2 + 15x – 9 = 0

Find all roots and factor completely

Answer 1

find the rational roots, and use that to find the irrational and imaginary roots

Answer 2

do u know the rational root theorem?

Answer 3

\[2x ^{4} + 5x ^{3} + 3x ^{2} +15x - 9 = 0 \]
\[(2x ^{4} +3x ^{2} - 9) + (5x ^{3} + 15x) = 0\]
\[(x ^{2} + 3)(2x ^{2} - 3) + (5x)(x ^{2} + 3) = 0\]
\[(x ^{2} + 3)(5x + 2x ^{2} - 3) = 0\]
\[(x ^{2} + 3)(x +3)(2x - 1) = 0 \]
\[x _{1} = -3\]
\[x _{2} = .5\]