How do you find the roots, real and imaginary, of y=8x2−15x−4−2(3x+3)2 using the quadratic formula?

1 Answer
Roella W.
Jan 12, 2016

x≈−4.83 or x≈−0.27

Explanation:

First multiply out the terms so that the expression can be rearranged into standard form.
y=8x2−15x−4−2(9x2+18x+9)
y=8x2−18x2−15x−36x−4−9
y=−10x2−51x−13
For a quadratic expression y=ax2+bx+c the quadratic formula is x=−b±√b2−4ac2a
x=−(−51)±√(−51)2−4(−10)(−13)2(−10)
x=51±√2601−520−20
x=−51±√208120
Because the number under the square root sign is positive, there are no imaginary roots, only real ones.
x≈−51±45.6220
x≈−4.83 or x≈−0.27

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