Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $5 y ^ { 2 } + 6 y - 3 = 0$
A)nonreal complex numbers, complex conjugates
B)rational, unequal
C)irrational, unequal
D)rational, equal
E)irrational, equal

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation in the form of $ax^2+bx+c=0$ is $b^2-4ac$. In this case, the discriminant is $6^2-4(5)(-3)=96$. Since the discriminant is positive, the quadratic equation has two unequal real roots. Moreover, since the discriminant is not a perfect square, the roots will be irrational. Therefore, the answer is C: irrational, unequal.

Use the Discriminant to Determine What Type of Solutions Exist 5y2+6y−3=05 y ^ { 2 } + 6 y - 3 = 05y2+6y−3=0

Use the Discriminant to Determine What Type of Solutions Exist $5 y ^ { 2 } + 6 y - 3 = 0$