Use the discriminant to find the number and kind of solutions for the following equation.
A) D = 30, two irrational
B) D = - 16, two complex
C) D = 24, two rational
D) D = 25, two rational
E) D = 0, one rational

Question

Use the discriminant to find the number and kind of solutions for the following equation. 
A) D = 30, two irrational 
B) D = - 16, two complex 
C) D = 24, two rational 
D) D = 25, two rational 
E) D = 0, one rational

Quizplus · Accepted Answer

The discriminant of a quadratic equation in the form $ax^2+bx+c=0$ is given by $D=b^2-4ac$. If $D<0$, then there are two complex solutions, if $D=0$, then there is one real solution, and if $D>0$, then there are two real solutions. In this case, the discriminant is $D=(-2)^2-4(2)(3)=-16$, which means there are two complex solutions. Therefore, the best choice is (B).

Use the Discriminant to Find the Number and Kind of Solutions