Question

How do you solve `x^2 - 4x + 13=0` using the quadratic formula?

Answer 1

Solution: `x= 2+3i , x=2-3i`

Explanation:

Comparing with standard equation `ax^2+bx+c=0`, we get here `a=1, b=-4,c=13 ; D=b^2-4ac= 16-52= -36`.

Discriminant (D) is negative , so roots are complex in nature.

Roots are `x= -b/(2a) +- sqrt (b^2-4ac)/(2a) or x = 4/(2*1) +- sqrt (16-52)/(2*1) = 2+- (6*i)/2 = 2 +-3i`

Solution: `x= 2+3i , x=2-3i` [Ans]