Question

Use the quadratic formula to solve the equation -3x^2-x-3=0

Answer 1

`x_(1=) (-1+i√(35) )/(6) \\\\x_(2=) (-1-i√(35) )/(6)`

Explanation:

Using the quadratic formula:

`x=\frac{-b+-\sqrt{b^(2)-4*a*c} }{2*a}`

We will have two solutions:

`x_(1)\\ x_(2)`

-3x^2-x-3=0 a=-3 b=-1 c=-3

We have:

`x_(1)=(1+√(-35) )/(-6)\\\\x_(2)=(1-√(-35) )/(-6)\\`

we can write:

`x_(1)=(-1+√(-35) )/(6)\\\\x_(2)=(-1-√(-35) )/(6)\\`

The solutions are not real numbers.

So, we know:
`i=√(-1)`

Finally we have:

`x_(1)=(-1+i√(35) )/(6)\\\\x_(2)=(-1-i√(35) )/(6)\\`