Question

How do you find the discriminant for `2x^2-11x+10=0` and determine the number and type of solutions?

Answer 1

`Delta = sqrt41`, so `f` has two real zeroes.

Explanation:

We know that, for any quadratic polynomial of the form `ax^2+bx+c`, the discriminant, `Delta`, is given by `Delta= b^2-4ac`.

If `∆ > 0`, then the polynomial will have two real solutions.

If `∆=0`, then the polynomial will have one real solution - a double root.

And if `∆ < 0`, then the polynomial will have no real roots and two complex roots.

And if `∆` is a perfect square, then the polynomial will have rational roots.

For the given polynomial, `∆=(11^2-4xx2xx10)=41`. Since `∆ > 0`, but `sqrt∆ notin QQ`, the polynomial will have two real roots.