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How Do You Use The Discriminant to Determine the Number of Solutions of a Quadratic Equation?

Use the discriminant to determine if a quadratic equation has two solutions, one solution, or no solution.

Summary

  1. The discriminant is the expression under the radical in the quadratic formula
  2. Since the discriminant, 8, was positive, x2 - 2x - 1 has two solutions

Notes

    1. The discriminant is equal to b2 - 4ac
    1. a is the coefficient in front of x2
    2. b is the coefficient in front of x
    3. c is the constant term
    1. If the discriminant is positive, there will be two solutions
    2. If the discriminant is zero, there will be one solution
    3. If the discriminant is negative, there will be no real solutions