Question

When does a quadratic equation have no solutions

Answer 1

A quadratic equation has no solutions when the discriminant is negative.

Step-by-step explanation:

A quadratic equation has no solutions when the discriminant is negative. The discriminant is the expression inside the square root in the quadratic formula. If the discriminant is negative, it means that there are no real solutions to the equation. For example, the equation x^2 + 4 = 0 has no solutions because the discriminant is 4 - 4(1)(4) = -12.

Answer 2

A quadratic equation has solutions when the graph crosses the x-axis. There are two ways the graph can have no solution, when the "a" value is greater than 0 and is translated vertically above the x-axis, or if the opposite occurs, when the "a" value is negative and is translated vertically below the x-axis.