Question

How do you find the discriminant and how many solutions does ## have?

Answer 1

Explanation:

Discriminant of a Quadratic.
The number `color(brown)(D = b^2 – 4ac)` determined from the coefficients of the equation ax^2 + bx + c = 0.

The discriminant reveals what type of roots the equation has. Note: b^2 – 4ac comes from the quadratic formula.

1. `color(blue)(b^2 −4ac = 0, " There is one real root. "`

2. `color(green)(b^2 −4ac > 0, " There are two real roots. "`

3. `color(red)(b^2 - 4ac < 0, " If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis."`