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Ch. 3 - Polynomial and Rational Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 3 - Polynomial and Rational FunctionsProblem 83
Chapter 4, Problem 83

Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x2+4x+6=0

Verified step by step guidance
1
Identify the type of equation given. Here, the equation is a quadratic equation of the form x2 + 4x + 6 = 0, where the highest power of x is 2.
Recall the quadratic formula, which is used to solve any quadratic equation ax2 + bx + c = 0. The formula is x = rac{-b \(\u\)00b1 21212121b^2 - 4ac}{2a}.
Identify the coefficients from the equation: a = 1, b = 4, and c = 6.
Substitute the values of a, b, and c into the quadratic formula: x = rac{-4 21212121 21212121 4^2 - 4(1)(6)}{2(1)}.
Simplify the expression under the square root (the discriminant) and then simplify the entire expression to find the two possible values of x.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Quadratic Equations

A quadratic equation is a polynomial equation of degree two, generally written as ax² + bx + c = 0. It represents a parabola when graphed, and solving it means finding the values of x that satisfy the equation.
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Completing the Square

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x + p)² = q. This technique transforms the quadratic into a perfect square trinomial, making it easier to solve for x.
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Quadratic Formula

The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), provides a direct way to find the roots of any quadratic equation ax² + bx + c = 0. It uses the coefficients to calculate the solutions, including complex roots when the discriminant is negative.
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Related Practice
Textbook Question

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x2+x−6)/(x−3)

Textbook Question

Exercises 82–84 will help you prepare for the material covered in the next section. Let f(x)=an(x4−3x2−4). If f(3)=−150, determine the value of a_n.

Textbook Question

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x2+1)/x

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Textbook Question

In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x2−1)/x

Textbook Question

Find the inverse of f(x)=(x−10)/(x+10).

Textbook Question

Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x2+4x−1=0