Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $$4 y ^ { 2 } + y + 5 = 0$$
A)rational, equal
B)irrational, unequal
C)irrational, equal
D)nonreal complex numbers, complex conjugates
E)rational, unequal

Question

Quizplus · Accepted Answer

The discriminant of the quadratic equation $ax^2+bx+c=0$ is given by $b^2-4ac$. If the discriminant is negative, then the solutions will be nonreal complex numbers and will be complex conjugates of each other. In this case, the discriminant is $1-4(4)(5)=-79$, which is negative. Therefore, the solutions will be nonreal complex numbers and complex conjugates of each other. The correct choice is D.

Use the Discriminant to Determine What Type of Solutions Exist 4y2+y+5=04 y ^ { 2 } + y + 5 = 04y2+y+5=0

Use the Discriminant to Determine What Type of Solutions Exist $4 y ^ { 2 } + y + 5 = 0$