Question

find the rational roots of the polynomial P(x)= 2x^4-3x^3-9x^2+15X-5, then use this information to solve the following equation 2x^4-3x^3-9x^2+15x-5=0.

Answer 1

\[2x^4-3x^3-9x^2+15x-5=\]\[=2x^4-2x^3-x^3+x^2-10x^2+10x+5x-5=\]\[=(x-1)(2x^3-x^2-10x+5)=\]\[=(x-1)(x^2(2x-1)-5(2x-1))=(x-1)(2x-1)(x^2-5)\]