How do you find the roots, real and imaginary, of y=-2(x +3)^2-5x + 6 using the quadratic formula?

1 Answer
Alan P.
Feb 16, 2016

Roots: x in {-7.723, -0.777}

Explanation:

First convert the given equation:
y=-2(x+3)^2-5x+6 into standard quadratic form:

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

y=-2x^2-12x-18-5x+6

y=-2x^2-17x-12

Apply the quadratic formula:
color(white)("XXX")x=(-b+-sqrt(b^2-4ac))/(2a)
with a=-2, b=-17, and c=-12

x=(17+-sqrt(17^2-4(2)(12)))/(2(-2)
which (with a bit of arithmetic) gives:
color(white)("XXX")x~~-7.723 or x~~-0.777

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