How do you find the roots, real and imaginary, of y=x(x-1)-(3x-1)^2 using the quadratic formula?

1 Answer
James
Jun 25, 2018

Expand and simplify to find the equation in standard form, then apply the quadratic formula to obtain the roots: x=(5+-isqrt(7))/16.

Explanation:

The quadratic formula can be used with quadratic equations in standard form, y=ax^2+bx+c.

First expand and simplify the given equation to rearrange it into standard form.

y=x(x-1)-(3x-1)^2
y=x^2-x-(9x^2-6x+1)
y=x^2-x-9x^2+6x-1
y=-8x^2+5x-1

This equation is now in standard form, where a=-8, b=5, and c=-1.

To solve for the roots of the equation, set y=0:
0 = -8x^2+5x-1,

Apply the quadratic formula:
x = (-b+-sqrt(b^2-4ac))/(2a)
x = (-(5)+-sqrt((5)^2-4(-8)(-1)))/(2(-8))
x = (-5+-sqrt(-7))/-16
x=(5+-sqrt(-7))/16
x=(5+-sqrt(-1)sqrt(7))/16
x=(5+-isqrt(7))/16

Related questions
See all questions in Quadratic Formula
Impact of this question
1758 views around the world
You can reuse this answer
Creative Commons License