Question

Find the zeros (roots) of the following equations. f(x) = 2x5 - 9x4 + 12x3 - 12x2 + 10x - 3 = 0

Answer 1

Hi,
$f(1)=2*1^5-9*1^4+12*1^3-12*1^2+10*1-3\\ =2-9+12-12+10-3\\ =0\\ f(x)=(x-1)(2x^4-7x^3+5x^2-7x+3)\\ g(x)=2x^4-7x^3+5x^2-7x+3\\ g(3)=2*3^4-7*3^3+5*3^2-7*3+3\\ =162-189+45-21+3\\ =0\\ g(x)=(x-3)(2x^3-x^2+2x-1)\\ h(x)=2x^3-x^2+2x-1\\ h( \dfrac{1}{2} )=2* \dfrac{1}{8} - \dfrac{1} {4}+1-1\\ =0\\ h(x)=(2x-1)(x^2+1)\\ f(x)=(x-1)(x-3)(2x-1)(x+i)(x-i)$
Roots are 1,3,0.5,i,-i.