Question

What is the discriminant of `3x^2+6x=2`?

Answer 1

See a solution process below:

Explanation:

First, we need to rewrite the equation in standard quadratic form:

`3x^2 + 6x - color(red)(2) = 2 - color(red)(2)`

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

The quadratic formula states:

For `ax^2 + bx + c = 0`, the values of `x` which are the solutions to the equation are given by:

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`

The discriminate is the portion of the quadratic equation within the radical: `color(blue)(b)^2 - 4color(red)(a)color(green)(c)`

If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions

To find the discriminant for this problem substitute:

`color(red)(3)` for `color(red)(a)`

`color(blue)(6)` for `color(blue)(b)`

`color(green)(-2)` for `color(green)(c)`

`color(blue)(6)^2 - (4 * color(red)(3) * color(green)(-2)) =>`

`36 - (-24) =>`

`36 + 24 =>`

`60`

Because the discriminate in positive there would be two real solutions for this problem.