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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

10. Roots and Zeros

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Exercise 1 Page 77

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.

Roots: x=5, x=- 2
Number and Type of Roots: two real roots

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 a We first need to identify the values of a, b, and c. x^2-3x-10=0 ⇕ 1x^2+( - 3)x+( - 10)=0 We see that a= 1, b= - 3, and c= - 10. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -3)±sqrt(( - 3)^2-4( 1)( - 10))/2( 1)

▼

Simplify

- (- a)=a

x=3±sqrt((- 3)^2-4(1)(- 10))/2(1)

Calculate power

x=3±sqrt(9-4(1)(- 10))/2(1)

Identity Property of Multiplication

x=3±sqrt(9-4(- 10))/2

MultNegNegOnePar

- a(- b)=a* b

x=3±sqrt(9+40)/2

Add terms

x=3±sqrt(49)/2

Calculate root

x=3±7/2

The roots of the given equation are x= 3± 72. Let's separate them into the positive and negative cases.

x=3± 7/2
x_1=3+7/2	x_2=3-7/2
x_1=10/2	x_2=- 4/2
x_1=5	x_2=- 2

Using the Quadratic Formula, we found that the roots of the given equation are x=5 and x=- 2, both of which are real.

Subchapter links

Exercises p.77-79