Question

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

Answer 1

Roots are complex conjugate pair `x=(5+isqrt15)/10` and `(5-isqrt15)/10`

Explanation:

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

The solution of equation `ax^2+bx+c=0` are given by `x=((-b+-sqrt(b^2-4ac))/(2a))`.

As `a=-5, b=5 and c=-2`,

`x=((-5+-sqrt((-5)^2-4*(-5)*(-2)))/(2(-5)))`.or

`x=((-5+-sqrt(25-40))/(-10))` or

`x=((5+-sqrt(-15))/10)` or

`x=((5+-isqrt15)/10)`

Hence, roots are complex conjugate pair `(5+isqrt15)/10` and `x=(5-isqrt15)/10`