For a quadratic equation ax^2 + bx + c = 0, the product of the roots is given by which expression?

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 $24.99Unlock all

Prepare for the PSAT 8/9 Math Test. Engage with flashcards and multiple-choice questions, featuring hints and explanations for each question to help you succeed. Be exam-ready!

Multiple Choice

For a quadratic equation ax^2 + bx + c = 0, the product of the roots is given by which expression?

Explanation:
The product of the roots is c/a. For a quadratic ax^2 + bx + c = 0 with a ≠ 0, you can think of it as a(x − r)(x − s) where r and s are the roots. Expanding gives ax^2 − a(r + s)x + a(rs). By matching coefficients with ax^2 + bx + c, you get the product rs = c/a and the sum r + s = −b/a. So the product is c/a. This is a direct result of how a quadratic factors and how the coefficients relate to the roots.

The product of the roots is c/a. For a quadratic ax^2 + bx + c = 0 with a ≠ 0, you can think of it as a(x − r)(x − s) where r and s are the roots. Expanding gives ax^2 − a(r + s)x + a(rs). By matching coefficients with ax^2 + bx + c, you get the product rs = c/a and the sum r + s = −b/a. So the product is c/a. This is a direct result of how a quadratic factors and how the coefficients relate to the roots.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy