How do you find the roots, real and imaginary, of y=−5x2+5x−2 using the quadratic formula?

1 Answer
Shwetank Mauria
Feb 18, 2016

Roots are complex conjugate pair x=5+i√1510 and 5−i√1510

Explanation:

By finding the roots, real and imaginary, of y=−5x2+5x−2, means finding zeros of the function y=−5x2+5x−2 or solving the equation −5x2+5x−2=0.

The solution of equation ax2+bx+c=0 are given by x=(−b±√b2−4ac2a).

As a=−5,b=5andc=−2,

x=⎛⎜ ⎜⎝−5±√(−5)2−4⋅(−5)⋅(−2)2(−5)⎞⎟ ⎟⎠.or

x=(−5±√25−40−10) or

x=(5±√−1510) or

x=(5±i√1510)

Hence, roots are complex conjugate pair 5+i√1510 and x=5−i√1510

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