Final answer:
To solve x³+4x²−x using the quadratic formula, rearrange the equation into the form ax²+bx+c = 0, substitute the values of a, b, and c into the quadratic formula, and simplify to find the solutions for x, which are -2+√5 and -2-√5.
Step-by-step explanation:
To solve the equation x³+4x²−x using the quadratic formula, we first rearrange the equation to the form ax²+bx+c = 0. In this case, a = 1, b = 4, and c = -1. Then, we substitute these values into the quadratic formula and simplify to find the solutions for x.
The quadratic formula is:
x = (-b ± √(b²-4ac)) / (2a)
Substituting the values of a, b, and c, we get:
x = (-4 ± √(4²-4(1)(-1))) / (2(1))
Simplifying further:
x = (-4 ± √(16+4)) / 2
x = (-4 ± √(20)) / 2
x = (-4 ± √(4*5)) / 2
x = (-4 ± 2√5) / 2
x = -2 ± √5