Question

Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
2x2 + 6x – 7 = 0

Answer 1

The discriminant of a quadratic equation is b^2 - 4ac, where the quadratic is ax^2 + bx + c = 0.

If the discriminant is positive, there are two rational solutions,
If the discriminant is zero, we get one rational solution,
and a negative discriminant means two imaginary solutions.