Math - Find all roots
posted by Amy on .
Find all roots:
#1.) 2x^3 + 5x^2 - 22x + 15 = 0
#2.) x^4 + 4x^3 + 6x^2 + 8x + 8 = 0
2x^3 + 5x^2 - 22x + 15 = 0
Did you notice that the coefficients of the equation add up to zero?
This means that (x-1) is a factor.
Divide the left-hand-side by (x-1) using long division and solve the resulting quadratic equation by factoring.
If the coefficient of x^4 is 1 and the constant term is 8, the possible real rational factors are (x+1), (x+2), (x+4) or (x+8). Try these factors and reduce the expression by long division. Repeat until no more factors can be found.
Hint: there are two complex roots for this equation, so you will only find two real roots.