Question

How many roots can a quadratic equation have

Answer 1

Step-by-step explanation:

It all depends on the discriminants sign.

The quadratic equation:

$ax^2+bx+c=0$

The discriminant:

$\Delta=b^2-4ac$

If Δ < 0, then the equation has no real solution

If Δ = 0, then the equation has one solution $x=\dfrac{-b}{2a}$

If Δ > 0, then the equation has two different solution

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Answer 2

Answer:

2 roots, 1 root, or no roots

Step-by-step explanation:

There is a maximum of two roots

If the maximum or minimum is on the x-axis there is 1 repeated root

The roots are imaginary if it does not touch the x-axis