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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Using the Distributive Property

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Exercise 53 Page 41

Use the Zero Product Property.

a, b∈ R, a≠ 0

Practice makes perfect

We are asked to solve the equation for x. (ax+b)(ax-b)=0 To solve this equation, we will apply the Zero Product Property.

(ax+b)(ax-b)=0

Use the Zero Product Property

lcax+b=0 & (I) ax-b=0 & (II)

▼

(I), (II): Solve for x

(I): LHS-b=RHS-b

lcax=- b & (I) ax-b=0 & (II)

(I): .LHS /a.=.RHS /a.

lcx=- ba & (I) ax-b=0 & (II)

(II): LHS+b=RHS+b

lcx=- ba & (I) ax=b & (II)

(II): .LHS /a.=.RHS /a.

lcx=- ba & (I) x= ba & (II)

The solutions to the equation are - ba and ba. Since denominators cannot be zero, a≠ 0 while b can be any real number.

Subchapter links

Exercises p.39-42