Use the discriminant to find what type of solutions (two rational, two irrational, one rational, or two nonreal complex)
each of the following equations has. Do not solve the equation.
-$$7 + 2 x ^ { 2 } = 3 x$$
A) two irrational solutions
B) one rational solution
C) two nonreal complex 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 $7 + 2x^2 = 3x$, rearranging it into standard form gives $2x^2 - 3x + 7 = 0$, where $a = 2$, $b = -3$, and $c = 7$. The discriminant is $(-3)^2 - 4(2)(7) = 9 - 56 = -47$. Since the discriminant is negative, the equation has two nonreal complex solutions, which contradicts my initial calculation. The correct answer should be two nonreal complex solutions, indicating an error in my initial response.

Use the Discriminant to Find What Type of Solutions (Two 7+2x2=3x7 + 2 x ^ { 2 } = 3 x7+2x2=3x

Use the Discriminant to Find What Type of Solutions (Two $7 + 2 x ^ { 2 } = 3 x$