Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve.
-$s^{2}-7 s+6=0$
A) Two rational solutions
B) One rational solution
C) Two irrational solutions
D) Two nonreal complex solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the equation $s^2 - 7s + 6 = 0$, the discriminant is $(-7)^2 - 4(1)(6) = 49 - 24 = 25$. Since the discriminant is a perfect square and positive, the equation has two rational solutions.

Use the Discriminant to Determine Whether the Equation Has Two s2−7s+6=0s^{2}-7 s+6=0s2−7s+6=0

Use the Discriminant to Determine Whether the Equation Has Two $s^{2}-7 s+6=0$