Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real
solution.
-
A) one real solution
B) two real solutions
C) no real solution

Question

Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real
solution.
-
A) one real solution 
B) two real solutions 
C) no real solution

Quizplus · Accepted Answer

We can use the quadratic formula to find the solutions of the equation: 
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
The discriminant is the expression inside the square root, $b^2-4ac$. If the discriminant is positive, then there are two distinct real solutions. If the discriminant is zero, then there is a single real solution. If the discriminant is negative, then there are no real solutions. In this case, the discriminant is $10^2-4(1)(-5)=120$, which is positive. Therefore, there are two distinct real solutions. The discriminant of the equation is greater than 0, which indicates that there are two distinct real solutions.

Use the Discriminant to Determine Whether the Equation Has Two