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

lemjay | High School Teacher | (Level 2) Senior Educator

Posted on

`-3x^2+6x-7=0`

The discriminant of this equation is:

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

discriminant`=-48`

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=(-b+-sqrt(b^2-4ac))/(2a)=(-6+-sqrt(6^2-4(-3)(-7)))/(2(-3))`

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

`x=(-2(3+-2isqrt3))/(-6)=(3+-2isqrt3)/3`

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

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

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

`(3+2isqrt(3))/(3)`

`(3-2isqrt(3))/(3)`