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Core Connections Algebra 2, 2013 View details

3. Section 8.3

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Exercise 171 Page 428

Practice makes perfect

a Let's start by setting the polynomial equal to 0 and solving the equation.

x^2-10=0

AddEqn

LHS+10=RHS+10

x^2=10

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± sqrt(10)

The equation has two roots. With this information, we can factor the expression by substituting a= sqrt(10) and b= - sqrt(10) in the expression (x- a)(x- b). (x- sqrt(10))(x-( - sqrt(10))) ⇓ (x-sqrt(10))(x+sqrt(10))

b Again, we will start by setting the equation equal to zero.

x^2-3x-7=0To solve this equation we can use the Quadratic Formula.

x^2-3x-7=0

UseQuadForm

Use the Quadratic Formula: a = 1, b= - 3, c= -7

x=-( -3) ± sqrt(( - 3)^2-4( 1)( -7))/2( 1)

▼

Solve for x

NegNeg

- (- a)=a

x=3± sqrt((- 3)^2-4(1)(-7))/2( 1)

CalcPowProd

Calculate power and product

x=3± sqrt(9+28)/2

AddTerms

Add terms

x=3± sqrt(37)/2

StateSol

State solutions

lx_1=.(3+sqrt(37)) /2. x_2=.(3-sqrt(37)) /2.

The equation has two roots. With this information, we can factor the expression by substituting a= 3+sqrt(37)2 and b= 3-sqrt(37)2 into the form (x- a)(x- b). (x- 3+sqrt(37)2)(x- 3-sqrt(37)2)

c Let's start by setting the polynomial equal to 0 and solving the equation.

x^2+4=0

SubEqn

LHS-4=RHS-4

x^2=- 4

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± sqrt(- 4)

SqrtNegToISqrt

sqrt(- a)= isqrt(a)

x=± isqrt(4)

CalcRoot

Calculate root

x=± i2

CommutativePropMult

Commutative Property of Multiplication

x=± 2i

The equation has two roots. With this information, we can factor the expression by substituting a= 2i and b= - 2i in the form (x- a)(x- b). (x- 2i)(x-( - 2i)) ⇓ (x-2i)(x+2i)

d Again, we will start by setting the equation equal to zero.

x^2-2x+2=0To solve this equation, we can use the Quadratic Formula.

x^2-2x+2=0

UseQuadForm

Use the Quadratic Formula: a = 1, b= -2, c= 2

x=-( -2) ± sqrt(( - 2)^2-4( 1)( 2))/2( 1)

▼

Solve for x

NegNeg

- (- a)=a

x=2± sqrt((- 2)^2-4(1)(2))/2(1)

CalcPowProd

Calculate power and product

x=2± sqrt(4-8)/2

SubTerm

Subtract term

x=2± sqrt(- 4)/2

SqrtNegToISqrt

sqrt(- a)= isqrt(a)

x=2± isqrt(4)/2

CalcRoot

Calculate root

x=2± i2/2

CommutativePropMult

Commutative Property of Multiplication

x=2± 2i/2

StateSol

State solutions

lcx=.(2+2i) /2. & (I) x=.(2-2i) /2. & (II)

(I), (II): Calculate quotient

lx_1=1+i x_2=1-i

The equation has two roots. With this information, we can factor the expression by substituting a= 1+i and b= 1-i in the form (x- a)(x- b). (x-( 1+i))(x-( 1-i))