Question

How can you tell when a quadratic equation has two identical, rational solutions?

when the radicand is negative

when b in the quadratic formula is greater than the radicand

when the radicand equals zero

when the radicand is not a perfect square

Answer 1

@SolomonZelman

Answer 2

If we look at the quadratic equation
\[ x = \frac{-b \pm \sqrt{b-4ac}}{2a} \]
Notice that the only time you will obtain different answers is when the radicand is a non zero value, since technical this gives us
\[ x_{1} = \frac{-b + \sqrt{b-4ac}}{2a} \text{ or } x_{2} = \frac{-b - \sqrt{b-4ac}}{2a} \]

These are two solutions that are unique for the quadratic

If however
\[ \sqrt{b-4ac}=0 \]
Then we get:
\[ x_{1} = \frac{-b}{2a} \text{ or } x_{2} = \frac{-b }{2a} \]
So x_1 = x_2 when the radicand is zero

Answer 3

Thank you