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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. The Quadratic Formula and the Discriminant

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Exercise 1 Page 194

Make sure you write all the terms on the left-hand side of the equation and simplify as much as possible before using the Quadratic Formula.

(- 6+3sqrt(5), - 6-3sqrt(5))

Practice makes perfect

We will use the Quadratic Formula to solve the given quadratic equation. ax^2+ bx+ c=0 ⇔ x=- b± sqrt(b^2-4 a c)/2 aWe first need to identify the values of a, b, and c. x^2+12x-9=0 ⇔ 1x^2+ 12x+( - 9)=0 We see that a= 1, b= 12, and c= - 9. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 12±sqrt(12^2-4( 1)( - 9))/2( 1)

▼

Solve for x and Simplify

Calculate power

x=- 12±sqrt(144-4(1)(- 9))/2(1)

a * 1=a

x=- 12±sqrt(144-4(- 9))/2

MultNegNegOnePar

- a(- b)=a* b

x=- 12±sqrt(144+36)/2

Add terms

x=- 12±sqrt(180)/2

SplitIntoFactors

Split into factors

x=- 12±sqrt(36* 5)/2

sqrt(a* b)=sqrt(a)*sqrt(b)

x=- 12± sqrt(36)* sqrt(5)/2

Calculate root

x=- 12± 6 sqrt(5)/2

Factor out 2

x=2(- 6± 3sqrt(5))/2

CancelCommonFac

Cancel out common factors

x=- 6± 3sqrt(5)

Using the Quadratic Formula, we found that the solutions of the given equation are x=- 6± 3sqrt(5). Therefore, the solutions are x_1=- 6+3sqrt(5) and x_2=- 6-3sqrt(5).

Subchapter links

Exercises p.194-197