Question

What is the discriminant of the quadratic equation `4x^2+7x+4=0`?

Answer 1

`-207`
The equation has 2 imaginary solutions

Explanation:

The discriminant is part of the quadratic formula and is used to find how many and what type of solutions a quadratic equation has.

Quadratic formula:

`(-b+-sqrt(b^2-4ac))/(2a)`

Discriminant:

`b^2-4ac`

Quadratic equation written in standard form:

`ax^2+bx+c`

That means that, in this situation, `a` is 4, `b` is 7, and `c` is 4

Plug those numbers into the discriminant and evaluate:

`7^2-4*4*4`

`49-4*4*4`

`49-256`

`-207 rarr` Negative discriminants indicate that the quadratic equation has 2 imaginary solutions (involving `i`, the square root of -1)

Positive discriminants indicate that the quadratic equation has 2 real solutions (no `i`)

Discriminants of 0 indicate that the quadratic equation has 1 real solution (perfect square, such as `x^2-12x+36`)