# How do you find value of discriminant then describe number and type of solutions for x^2 - 6x +3 = 0?

Jul 6, 2016

The roots are real, different and irrational.

#### Explanation:

We can work out what type of roots an equation has by finding the discriminant. It is called $\Delta \text{ (delta)}$

In $a {x}^{2} + b x + c \text{ } \Delta = {b}^{2} - 4 a c$,

If $\Delta < 0 ,$then the roots are imaginary, (non-real).

If $\Delta = 0 ,$then the roots are real and equal. (ie one root)

If $\Delta > 0 ,$then the roots are real, different and irrational.

If $\Delta > 0 ,$and is a perfect square, (1, 4, 9, 16 ......) then the roots are real, different and rational.

In this example: $\Delta = {\left(- 6\right)}^{2} - 4 \left(1\right) \left(3\right) = 24$

The roots are real, different and irrational.