Question

What is the discriminant of the quadratic equation 3 – 4x = –6x2?

Answer 1

The discriminant is the stuff under the square root in the quadratic equation. Let's first get this equation in standard form. This must equal 0! Let's see what we have:

`3-4x=-6x^2`

Since we need this quadratic to equal 0 to use the quadratic formula, add
`6x^2` to both sides.

`6x^2-4x+3=0`

Note that I just rearranged the -4 and +3 to make it in the
`ax^2+bx+c` form. Now, let's put this in the quadratic equation.

`x=(4 +√((-4)^2-4(6)(3)) )/(2(6))`

Since we are only solving for the discriminant, let's simplify the expression under the square root.

`√((-4)^2-4(6)(3))`

`√(16-72)`

`√(-56)`

Now, since we have a negative number in the discriminant, we know that neither of the solutions will be real numbers. They will be in terms of
`i` (
`i=√(-1)`)

The simplified version of the discriminant is:

`2i√(14)`

However, if you have not learned imaginary numbers yet, you can say the discriminant is -56.