Use the discriminant to find the number and kind of solutions for the following equation.

Question

Quizplus · Accepted Answer

The discriminant is the term inside the square root in the quadratic formula, which is given by $b^2-4ac$. In this case, the quadratic equation is not given, but we are given the value of the discriminant.

If the discriminant is positive and a perfect square, then there are two rational roots. The only answer choice that fits this criteria is B, since $\sqrt{1296}=36$ is a perfect square.

If the discriminant is positive but not a perfect square, then there are two irrational roots. Option E fits this criteria, but since option B is also correct, we must choose both B and E.

If the discriminant is zero, then there is one real root (which may or may not be rational). Option D is incorrect since the discriminant is not zero.

If the discriminant is negative, then there are two complex roots. Option A and C fit this criteria, but they are not correct since the discriminant is not a multiple of 4, which would make it a perfect square.

Therefore, the best choice(s) are B and E, since they are the only options that match the given discriminant and correspond to possible types of roots for a quadratic equation.

Use the Discriminant to Find the Number and Kind of Solutions