Ch. 3 - Polynomial and Rational Functions

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

Blitzer 8th Edition

Ch. 3 - Polynomial and Rational Functions

문제 83

4장, 문제 83

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

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Identify the type of equation given. Here, the equation is a quadratic equation of the form

x 2 + 4x + 6 = 0

, where the highest power of

x

is 2.

Recall the quadratic formula, which is used to solve any quadratic equation

ax 2 + bx + c = 0

. The formula is

= 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

비슷한 문제에 대한 검증된 영상 답변:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

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