Explain how you would solve ( x − 2 ) ( x − 7 ) = 0 and also how you would solve ( x − 2 ) ( x − 7 ) = 4 .

Q: Expert Answer

To determine To explain: The choices of method to solve the given quadratic equations. Explanation There are three major methods for solving a quadratic equation- a. Factoring- The standard form for a quadratic equation in one variable is a x 2 + b x + c = 0 , where a , b , and c are real numbers and a ≠ 0 . This quadratic equation can be solved by factoring by applying the property, a b = 0 if and only if a = 0 or b = 0 . b. Completing the square- Transform the quadratic equation in the form x 2 + b x = k , square one half of b and add to each side of the equation then factor the left side and apply the property x 2 = a if and only if x = ± a . c. Quadratic formula- Any quadratic equation of the form a x 2 + b x + c = 0 , where a ≠ 0 , can be solved by the quadratic formula, x = − b ± b 2 − 4 a c 2 a . Given: The given quadratic equations are, ( x − 2 ) ( x − 7 ) = 0 and ( x − 2 ) ( x − 7 ) = 4 . Formula used: The solution of the equation a x 2 + b x + c = 0 is given by, x = − b ± b 2 − 4 a c 2 a Calculation: The given quadratic equation is, ( x − 2 ) ( x − 7 ) = 0 This equation can be solved by factoring, by applying the property, a b = 0 if and only if a = 0 or b = 0 . Using the property of factorization, x − 2 = 0 x = 2 Or, x − 7 = 0 x = 7 The solution set is { 2 , 7 }

Question

Still sussing out bartleby?

Answer 1

BuyFind

Intermediate Algebra

10th Edition

Jerome E. Kaufmann + 1 other

Publisher: Cengage Learning

ISBN: 9781285195728

Solutions

Chapter

Section

Answer 2

BuyFind

Intermediate Algebra

10th Edition

Jerome E. Kaufmann + 1 other

Publisher: Cengage Learning

ISBN: 9781285195728

Solutions

Chapter

Section

Answer 3

Solutions

Chapter

Section

Answer 4

Chapter

Section

Answer 5

To determine

To explain:

The choices of method to solve the given quadratic equations.

Explanation of Solution

There are three major methods for solving a quadratic equation-

a. Factoring- The standard form for a quadratic equation in one variable is ax2+bx+c=0, where a, b, and c are real numbers and a≠0. This quadratic equation can be solved by factoring by applying the property, ab=0 if and only if a=0 or b=0.

b. Completing the square- Transform the quadratic equation in the form x2+bx=k, square one half of b and add to each side of the equation then factor the left side and apply the property x2=a if and only if x=±a.

c. Quadratic formula- Any quadratic equation of the form ax2+bx+c=0, where a≠0, can be solved by the quadratic formula,

x=−b±b2−4ac2a.

Given:

The given quadratic equations are,

(x−2)(x−7)=0 and (x−2)(x−7)=4.

Formula used:

The solution of the equation ax2+bx+c=0 is given by,

x=−b±b2−4ac2a

Calculation:

The given quadratic equation is,

(x−2)(x−7)=0

This equation can be solved by factoring, by applying the property, ab=0 if and only if a=0 or b=0.

Using the property of factorization,

x−2=0x=2

Or,

x−7=0x=7

The solution set is {2,7}

Explain how you would solve ( x − 2 ) ( x − 7 ) = 0 and also how you would solve ( x − 2 ) ( x − 7 ) = 4 .

Intermediate Algebra

Solutions

Intermediate Algebra