Rational Root Theorem: Find g(x) = -5x^3 + x^2 + 5x – 1

Question

Find all roots of g(x).

g(x) = -5x³ + x² + 5x – 1^

Write your answer as a list of simplified values separated by commas, if there is more than one value. Make sure to include rational and irrational roots.

Answer 1

one root is x=1

divide the cubic by x-1 to get a quadratic: -5x^2 -4x +1

=-[5x^2+4x-1] = -(5x-1)(x+1)

set each factor =0

5x-1=0, x=1/5

x+1 = 0, x=-1

or use the quadratic formula

(5x+1)(x+1)

x = 4/-10 + or - (1/10)sqr(16+20) = -1, 1/5

roots are 1/5, 1 , -1