Question

How to use the discriminant to find out how many real number roots an equation has for `x^2 - 5x + 7 = 0`?

Answer 1

`x^2-5x+7` is of the form `ax^2+bx+c`, with `a=1`, `b=-5` and `c=7`.

The discriminant is given by the formula:

`Delta = b^2-4ac`

`= (-5)^2-(4xx1xx7) = 25-28 = -3`

Being negative, we can deduce that `x^2-5x+7=0` has no real roots (it has two distinct complex roots).