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

1 Answer
May 17, 2018

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.