Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$4 - 6 a ^ { 2 } = - 2 a + 1$
A) Two distinct irrational solutions
B) Two distinct nonreal complex solutions
C) One rational solution (a double solution)
D) Two distinct rational solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. First, we rewrite the given equation in the standard form: $6a^2 - 2a - 3 = 0$, where $a = 6$, $b = -2$, and $c = -3$. The discriminant is $(-2)^2 - 4(6)(-3) = 4 + 72 = 76$. Since the discriminant is positive and not a perfect square, the equation has two distinct irrational solutions.

Evaluate the Discriminant for the Equation 4−6a2=−2a+14 - 6 a ^ { 2 } = - 2 a + 14−6a2=−2a+1

Evaluate the Discriminant for the Equation $4 - 6 a ^ { 2 } = - 2 a + 1$