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

1 Answer
Feb 18, 2016

Answer:

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#