Return to Assignments Quadratic equations (abc-formula)

### Assignment 10

For which value(s) of does the equation::

have no solutions .

### Solution

When we want to know how many solutions a quadratic equation has, we look at the discriminant:

The equation may not have solutions, thus the discriminant has to be negative:

or:

We know that the graph of the function:

is an 'opens up' parabola which intersects the -axis in the points:

This parabola is positive if:

or