Question

How to use the discriminant to find out how many real number roots an equation has for `x^2 - 8x + 3 = 0`?

Answer 1

See a solution process below:

Explanation:

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)(1)` for `color(red)(a)`

`color(blue)(-8)` for `color(blue)(b)`

`color(green)(3)` for `color(green)(c)`

`color(blue)(-8)^2 - (4 * color(red)(1) * color(green)(2)) => 64 - 8 => 56`

`56` is positive therefore you would get two real solutions.