How do you solve #x^3 + 4x^2 - x# using the quadratic formula?

Question

Eva Adamson · Accepted Answer

#x={0,-2+-sqrt5}#

#x^3+4x^2-x=0# is a cubic equation. You first have to factor #x# out.

#[1]" "x^3+4x^2-x=0#

#[2]" "x(x^2+4x-1)=0#

The first root is #x=0# (from the #x# you factored out). You can use the quadratic formula to find the other two roots from #x^2+4x-1#.

#a=1# #b=4# #c=-1#

#[3]" "x=[-b+-sqrt(b^2-4ac)]/(2a)#

#[4]" "x=[-4+-sqrt(4^2-4(1)(-1))]/(2(1))#

#[5]" "x=[-4+-sqrt(20)]/2#

#[6]" "x=[-4+-2sqrt(5)]/2#

#[7]" "color(blue)(x=-2+-sqrt5)#

So the roots of the equation are:

#x={0,-2+-sqrt5}#

Savannah Anderson · Answer

undefined You cannot directly solve the equation x^3 + 4x^2 - x using the quadratic formula because it is a cubic equation, not a quadratic one. The quadratic formula is specifically for solving equations of the form ax^2 + bx + c = 0. To solve cubic equations, you typically use methods like factoring, synthetic division, or the cubic formula.