Which expression represents the solution for x in the quadratic equation Ax^2 + Bx + C = 0 using the quadratic formula?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $25.99Unlock all

Prepare for the Praxis Middle School Mathematics Exam with quizzes. Study with flashcards and multiple choice questions. Each question provides hints and detailed explanations. Ensure success on your test!

Multiple Choice

Which expression represents the solution for x in the quadratic equation Ax^2 + Bx + C = 0 using the quadratic formula?

Explanation:
The main idea is to use the quadratic formula to solve a quadratic equation in standard form. For Ax^2 + Bx + C = 0, the solution is x = [-B ± sqrt(B^2 − 4AC)] / (2A). This result comes from completing the square and shows how the coefficients A, B, and C determine the roots. Key parts to notice: the linear coefficient B is negated in front of the fraction, the expression under the radical is B^2 minus 4AC (the discriminant), and the denominator is 2A, reflecting the coefficient of x^2. This exact arrangement is what yields the correct roots for any quadratic with A ≠ 0. For illustration, with A = 1, B = −3, C = 2, the roots are x = [3 ± sqrt(9 − 8)]/2 = 1 and 2, which matches the factorization (x − 1)(x − 2) = 0. If any part is altered—such as using +4AC inside the radical or changing the denominator—the expression would no longer produce the correct roots.

The main idea is to use the quadratic formula to solve a quadratic equation in standard form. For Ax^2 + Bx + C = 0, the solution is x = [-B ± sqrt(B^2 − 4AC)] / (2A). This result comes from completing the square and shows how the coefficients A, B, and C determine the roots.

Key parts to notice: the linear coefficient B is negated in front of the fraction, the expression under the radical is B^2 minus 4AC (the discriminant), and the denominator is 2A, reflecting the coefficient of x^2. This exact arrangement is what yields the correct roots for any quadratic with A ≠ 0.

For illustration, with A = 1, B = −3, C = 2, the roots are x = [3 ± sqrt(9 − 8)]/2 = 1 and 2, which matches the factorization (x − 1)(x − 2) = 0. If any part is altered—such as using +4AC inside the radical or changing the denominator—the expression would no longer produce the correct roots.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy