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

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Answer 1 · 2015-10-25T10:22:30

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

$x^3+4x^2-x=0$ 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:

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

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