Question

match each discriminant value with the corresponding type of solutions it indicates. move one answer to each box. discriminant is less than 0 discriminant equals 0 discriminant is greater than 0 two real unequal roots two real equal roots two complex roots

Explanation:

For a quadratic equation $ax^2+bx+c=0$, the discriminant is $\Delta = b^2-4ac$.

1. When $\Delta < 0$, the square root of a negative number results in complex numbers, so there are two complex roots.
2. When $\Delta = 0$, the quadratic formula gives a single repeated real solution, so there are two real equal roots.
3. When $\Delta > 0$, the quadratic formula yields two distinct real values, so there are two real unequal roots.

Answer:

• discriminant is less than 0 → two complex roots
• discriminant equals 0 → two real equal roots
• discriminant is greater than 0 → two real unequal roots