Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.
A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) irrational, unequal
D) rational, equal
E) irrational, equal

Question

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 
A) nonreal complex numbers, complex conjugates 
B) rational, unequal 
C) irrational, unequal 
D) rational, equal 
E) irrational, equal

Quizplus · Accepted Answer

The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is b^2 - 4ac. If the discriminant is negative, the solutions will be nonreal complex numbers. If the discriminant is zero, the solutions will be rational and equal. If the discriminant is positive, the solutions will be either rational and unequal or irrational and unequal, depending on whether or not the square root in the quadratic formula can be simplified. In this case, we do not know the specific values of a, b, and c, but we do know that the discriminant is positive (because it is not specified as negative or zero). Therefore, the solutions will be either rational and unequal or irrational and unequal, and the best choice is C.

Use the Discriminant to Determine What Type of Solutions Exist