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The discriminant is the expression inside the radical in the quadratic formula, b 2 – 4 ac .

9.6. Applications of the Discriminant. Objectives: To use and apply the discriminant to find the number of solutions to a quadratic equation. The discriminant is the expression inside the radical in the quadratic formula, b 2 – 4 ac.

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The discriminant is the expression inside the radical in the quadratic formula, b 2 – 4 ac .

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  1. 9.6 Applications of the Discriminant Objectives: To use and apply the discriminant to find the number of solutions to a quadratic equation. The discriminant is the expression inside the radical in the quadratic formula, b2 – 4ac. • If b2 – 4ac is positive, then the equation has two solutions. • If b2 – 4acis zero, then the equation has one solution. • Ifb2 – 4acis negative, then the equation has no real solution.

  2. The discriminant also tells the number of times the parabola crosses the x-axis Positive discriminant: The parabola crosses x-axis twice. Zero discriminant: The parabola crosses x-axis once. Negative discriminant: The parabola never crosses x-axis. Positive Two solutions Negative No solutions Zero One solution

  3. Examples: Find the discriminant and determine the number of solutions a =1 b =-3 c =-4 1. 9 - -16 25 Two solutions a =1 b =2 c =5 2. 4 – 20 –16 No solutions 3. 16 – 16 0 One solution

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