Question

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

Answer 1

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 " (delta)"`

In `ax^2 + bx + c " "Delta = b^2 -4ac`,

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 = (-6)^2 - 4(1)(3) = 24`

The roots are real, different and irrational.