Question

How do you find the value of the discriminant and determine the nature of the roots `2p^2+5p-4`?

Answer 1

`Delta = 57 > 0` is not a perfect square, so the zeros are distinct, real and irrational.

Explanation:

Given:

`2p^2+5p-4`

Note that this is written in standard form:

`ap^2+bp+c`

with `a=2`, `b=5` and `c=-4`

The discriminant `Delta` is given by the formula:

`Delta = b^2-4ac`

`color(white)(Delta) = color(blue)(5)^2-4(color(blue)(2))(color(blue)(-4))`

`color(white)(Delta) = 25+32`

`color(white)(Delta) = 57`

Since `Delta > 0` the given quadratic has two distinct real zeros. Since `Delta = 57` is not a perfect square, those zeros are irrational.

The zeros of `2p^2+5p-4` are the roots of the equation:

`2p^2+5p-4 = 0`