Quadratic Formula and Discriminant

Learn and apply quadratic formula and discriminant using equations, examples, and interpretation.

Lesson 5 of 53 parts Practice Flashcards

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Quadratic Formula

Objective: Explain and use quadratic formula in an Algebra 1 problem.

For ax²+bx+c=0 with a≠0, x=(−b±√(b²−4ac))/(2a); substitute coefficients with their signs intact. Otherwise the equation is not quadratic and the denominator is zero.

Worked examples

Try itExample 1.1: Solve x²−7x+10=0. What is the larger root?Show answer

5. Factor the constructed trinomial, set each factor to zero, and compare roots. The answer is 5.

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Quadratic Formula

Objective: Explain and use quadratic formula in an Algebra 1 problem.

For ax²+bx+c=0 with a≠0, x=(−b±√(b²−4ac))/(2a); substitute coefficients with their signs intact. Otherwise the equation is not quadratic and the denominator is zero.

Worked examples

Try itExample 1.1: Solve x²−7x+10=0. What is the larger root?Show answer

5. Factor the constructed trinomial, set each factor to zero, and compare roots. The answer is 5.

Discriminant

Objective: Explain and use discriminant in an Algebra 1 problem.

D=b²−4ac is positive for two distinct real roots, zero for one repeated real root, and negative for no real roots. No, its square root is not real.

Worked examples

Try itExample 2.1: For x²−11x+24=0, compute the discriminant.Show answer

25. For this monic trinomial, the discriminant is the squared difference of its roots. The answer is 25.

Checking and Choosing Methods

Objective: Explain and use checking and choosing methods in an Algebra 1 problem.

Factoring, completing the square, and the formula can solve appropriate quadratics; verify candidate roots in the original equation. It works even when integer factoring is unavailable.

Worked examples

Try itExample 3.1: Solve x²−15x+44=0. What is the larger root?Show answer

11. Factor the constructed trinomial, set each factor to zero, and compare roots. The answer is 11.

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