Question

What is the discriminant of `2x^2 = 4x - 7` and what does that mean?

Answer 1

In the equation `ax^2+bx+c=0`, the discriminant is `b^2-4ac`

Explanation:

By completing the square it is possible to see that the solutions of the equation:

`ax^2+bx+c=0`

are of the form:

`x_1`=`(-b + sqrt(b^2-4ac))/(2a)` and

`x_2`=`(-b - sqrt(b^2-4ac))/(2a)`

So, to have solutions in the real numbers (as opposed to complex numbers), the square root `sqrt(b^2-4ac` must exist as a real number, and so we need `b^2-4ac>=0`.

In summary, to have real solutions, the discriminant `b^2-4ac` of the equation must satisfy `b^2-4ac>=0`