Question

How do you find the zeros of `y = 4.5x^2 – 1.5x + 1.5` using the quadratic formula?

Answer 1

`y` has no real zeroes, but its complex zeroes are `(3+-isqrt 87)/16`

Explanation:

The first thing we should check when trying to find the zeroes of a function is if its discriminant is greater than, equal to or less than zero.

`Delta_y = 1.5^2-4(4)(1.5)=-87/4`

`Delta_y < 0 therefore y` has no real roots.

However, we can still find its complex zeroes using the quadratic formula.

`x = (1.5+-sqrt(-1.5^2-4(4)(1.5)))/(2(4))=(3+-isqrt87)/16`