Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 6.2
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Exercise 92 Page 355

Practice makes perfect
a 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 Since all of the terms are on the left-hand side of the equation, we can identify the values of a, b, and c. 16x^2-8x+1=0 ⇔ 16x^2+( - 8)x+ 1=0 We see that a= 16, b= - 8, and c= 1. Let's substitute these values into the Quadratic Formula.
x=- b±sqrt(b^2-4ac)/2a
x=- ( - 8)±sqrt(( - 8)^2-4( 16)( 1))/2( 16)
â–Ľ
Solve for x and Simplify
x=8±sqrt((- 8)^2-4(16)(1))/2(16)
x=8±sqrt(64-4(16)(1))/2(16)
x=8±sqrt(64-64)/32
x=8±sqrt(0)/32
x=8± 0/32
Since adding or subtracting zero does not change the value of a number, the numerator will simplify to 8. Therefore, we will get only one value of x. x= 8/32 ⇔ x= 1/4 Using the Quadratic Formula, we found that the solution of the given equation is x= 14.
b 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 Since all of the terms are on the left-hand side of the equation, we can identify the values of a, b, and c. x^2+x+1=0 ⇔ 1x^2+ 1x+ 1=0 We see that a= 1, b= 1, and c= 1. Let's substitute these values into the Quadratic Formula.
x=- b±sqrt(b^2-4ac)/2a
x=- 1±sqrt(1^2-4( 1)( 1))/2( 1)
â–Ľ
Solve for x and Simplify
x=-1±sqrt(1-4(1)(1))/2(1)
x=-1±sqrt(1-4)/2
x=-1±sqrt(-3)/2
x=-1±sqrt(3(-1))/2
x=-1±sqrt(3) * sqrt(-1)/2
x=-1±sqrt(3)i/2
We have shown that our equation has two complex solutions. x_1=-1 + sqrt(3)i/2 and x_2=-1 - sqrt(3)i/2