Use the discriminant to predict the nature of the roots, then use the quadratic formula to find the roots. `-3x^2 + 6x - 7 = 0`

Expert Answers
lemjay eNotes educator| Certified Educator


The discriminant of this equation is:

discriminant`=b^2-4ac= 6^2-4(-3)(-7)=36-84`


Since it is less than zero, it indicates that the roots of the given equation are non-real numbers.

The values of the roots will be:


`x=(-6+-sqrt(-48))/(-6)=(-6+-isqrt48)/(-6) =(-6+-4isqrt3)/(-6)`


Hence, the roots are `x=(3+2isqrt3)/3` and `x=(3-2isqrt3)/3` .

atyourservice | Student

  use `b^2-4ac ` to find the discriminant

`6^2-4(-3)(-7)`  simplify it

`36-84=-48`    the discriminant is -48 meaning the problem has no real solutions as -48 is less that 0

to find the roots use the quadratic formula, you would end up with