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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Solving Quadratic Equations by Factoring

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Exercise 79 Page 176

Solve the equation by yourselves. Be careful about factorization.

Morgan is correct, see solution.

Practice makes perfect

Let's solve the equation by ourselves to decide if either of them is correct.

-12x^2+5x+2=0

Write as a sum

-12x^2+8x-3x+2=0

Factor out 4x

4x(-3x+2)-3x+2=0

Add parentheses

4x(-3x+2) +( -3x+2)=0

At this step, Gwen made a mistake by factorizing (-3x+2) incorrectly.

4x(-3x+2)+(-3x+2)=0

Factor out (-3x+2)

(4x+1)(-3x+2)=0

Use the Zero Product Property

l4x+1=0 -3x+2=0

(I): LHS-1=RHS-1

l4x=-1 -3x+2=0

(I): .LHS /4.=.RHS /4.

lx=-1/4 -3x+2=0

(II): LHS-2=RHS-2

lx=-1/4 -3x=-2

(II): .LHS /(-3).=.RHS /(-3).

lx=-1/4 x=2/3

As a result, Morgan is correct.

Subchapter links

Exercises p.174-177