Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real
solution, or no real solution without solving the equation.
-
A)repeated real solution
B)two unequal real solutions
C)no real solution

Question

Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real
solution, or no real solution without solving the equation.
-
A)repeated real solution 
B)two unequal real solutions 
C)no real solution

Quizplus · Accepted Answer

The discriminant, which is b^2 - 4ac, can be used to determine the nature of the roots of a quadratic equation. If the discriminant is greater than zero, then there are two unequal real solutions. If the discriminant is equal to zero, then there is a repeated real solution. If the discriminant is less than zero, then there are no real solutions. Without solving the equation given, we cannot determine the exact value of the discriminant, but we know that it is positive (since the equation has a solution), so the answer is B, two unequal real solutions. The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by b^2 - 4ac. If the discriminant is positive, then the equation has two unequal real solutions. If the discriminant is zero, then the equation has a repeated real solution. If the discriminant is negative, then the equation has no real solution. In this case, we are not given the coefficients of the quadratic equation, so we cannot calculate the discriminant. However, we are asked to determine the possible outcomes without solving the equation. The only choice that allows for two unequal real solutions is B, so the answer is B.

Use the Discriminant to Determine Whether the Quadratic Equation Has