Question

Mixed Practice. $$ 9 x^{2}-24 x+16=0 $$

   Mixed Practice.
$$
9 x^{2}-24 x+16=0
$$

Beginning Algebra

Beginning Algebra

Blair, Jamie;… 8th Edition

Chapter 12, Problem 28

Instant Answer

Solved by Expert Cameron Bunney

07/19/2020

Step 1

This is a quadratic equation because it has the form ax^2 + bx + c = 0, where a = 9, b = -24, and c = 16. Show more…

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Mixed Practice. $$ 9 x^{2}-24 x+16=0 $$

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Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of the second degree typically expressed in the standard form ax² + bx + c = 0 where a, b, and c are constants and a is not zero. They are fundamental in algebra and are solved by various methods including factoring, completing the square, or using the quadratic formula.

Discriminant

The discriminant of a quadratic equation, given by b² - 4ac, is a key concept that helps determine the nature of the roots of the equation. A positive discriminant indicates two distinct real roots, zero implies one real double root, and a negative value leads to two complex conjugate roots.

Factoring

Factoring is a method used to simplify quadratic equations by expressing them as a product of two binomials. This technique is often the quickest way to solve a quadratic when the polynomial can be factored into neat binomial factors that multiply to give the original quadratic expression.

Perfect Square Trinomial

A perfect square trinomial is a specific type of quadratic expression that can be written as the square of a single binomial. Recognizing a perfect square trinomial, such as one that fits the form (mx - n)², allows for a straightforward solution by setting the binomial equal to zero, revealing a repeated or double root.

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