Discriminant and Complex Solutions

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What is the discriminant of a quadratic equation?

Back

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) solutions.

Front

What does a discriminant of zero indicate about the roots of a quadratic equation?

Back

A discriminant of zero indicates that the quadratic equation has exactly one real solution (a repeated root).

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Front

What is another term for the zeros of a quadratic function?

Back

The zeros of a quadratic function are also called x-intercepts.

Front

If the discriminant is negative, what type of solutions can we expect?

Back

If the discriminant is negative, we can expect complex solutions.

Front

What is the formula for the discriminant in a quadratic equation?

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Front

How can you determine the nature of the roots of a quadratic equation using the discriminant?

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By evaluating the discriminant: if D > 0, two real solutions; D = 0, one real solution; D < 0, two complex solutions.