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.
-$\mathrm{v}^{2}-5 \mathrm{v}-2=0$
A) One rational solution
B) Two nonreal complex solutions
C) Two irrational solutions
D) Two rational 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 $v^2 - 5v - 2 = 0$, the discriminant is $(-5)^2 - 4(1)(-2) = 25 + 8 = 33$. Since 33 is positive and not a perfect square, the equation has two irrational solutions.

Use the Discriminant to Determine Whether the Equation Has Two v2−5v−2=0\mathrm{v}^{2}-5 \mathrm{v}-2=0v2−5v−2=0

Use the Discriminant to Determine Whether the Equation Has Two $\mathrm{v}^{2}-5 \mathrm{v}-2=0$