How do you find the roots, real and imaginary, of #y=(3x-4)(x+2)-x^2-x # using the quadratic formula?

1 Answer

Answer:

#:. x = (-1 + sqrt33) / 4 ~= 1.186#

#:. x = (-1 - sqrt33) / 4 ~= -1.686#

There are no imaginary roots.

Explanation:

Let's first simplify:

#y=(3x-4)(x+2)-x^2-x#

#y=3x^2+2x-8-x^2-x#

#y=2x^2+x-8#

Quadratic Formula:

# x = (-b \pm sqrt(b^2-4ac)) / (2a) #

with #a=2, b=1, c=-8#

# x = (-1 \pm sqrt(1^2-4(2)(-8))) / (2(2)) #

# x = (-1 \pm sqrt(1^2+32)) / 4 #

# x = (-1 \pm sqrt33) / 4 #

#:. x = (-1 + sqrt33) / 4 ~= 1.186#

#:. x = (-1 - sqrt33) / 4 ~= -1.686#

There are no imaginary roots.