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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
10. Roots and Zeros
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Exercise 17 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=- 2, x= 32
Number and Type of Roots: two real roots

Practice makes perfect

We will use the Quadratic Formula to find the roots of 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. 2x^2+x-6=0 ⇕ 2x^2+ 1x+( - 6)=0 We see that a= 2, b= 1, and c= - 6. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a
SubstituteValues

Substitute values

x=- 1±sqrt(1^2-4( 2)( - 6))/2( 2)
â–¼
Evaluate right-hand side
BaseOne

1^a=1

x=- 1±sqrt(1-4(2)(- 6))/2(2)
Multiply

Multiply

x=- 1±sqrt(1-8(- 6))/4
MultNegNegOnePar

- a(- b)=a* b

x=- 1±sqrt(1+48)/4
AddTerms

Add terms

x=- 1±sqrt(49)/4
CalcRoot

Calculate root

x=- 1± 7/4

The roots of this equation are x= - 1± 74. Let's separate them into the positive and negative cases.

x=- 1± 7/4
x_1=- 1+7/4 x_2=- 1-7/4
x_1=6/4 x_2=- 8/4
x_1=3/2 x_2=- 2

Using the Quadratic Formula, we found that the roots of the given equation are x_1= 32 and x_2=- 2. Both of them are real.

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