(b)
First write the equation in standard form- x^2 - 6 x+ 2 = 0 Subtract 6x.
- x^2 + 2 = 6 x
ax^2 +bx+c=0.- x^2 + 2 = 6 x
568 CHAPTER 9 Quadratic Equations
means- 1 x^2.
- x^2
Here, and(c)
The x-term is missing, so write the equation as follows.Then and(d)
Use the FOIL method.
2 x^2 +x- 5 = 0 Add 23; standard form2 x^2 +x- 28 =- 2312 x- 721 x+ 42 =- 23a=5,b=0, c=-12.5 x^2 + 0 x- 12 = 05 x^2 - 12 = 0a= - 1 ,b=- 6 , c= 2.The equation is
not in standard
form.OBJECTIVE 2 Use the quadratic formula to solve quadratic equations.To
develop the quadratic formula, we follow the steps given in Section 9.2for completing
the square on For comparison, we also show the corresponding
steps for solving (from Example 1(d)).Step 1 Transform so that the coefficient of the second-degree term is equal to 1.Divide by 2. Divide by a.Step 2 Write the equation so that the variable terms with xare alone on the left side.Add SubtractStep 3 Add the square of half the coefficient of xto each side, factor the left side,
and combine like terms on the right.Add Add.ax+b
2 ab2
=b^2 - 4 ac
4 a^2ax+1
4
b2
=41
16
b^2
4 a^2
x^2 +b
a
x+b^2
4 a^2=-
c
a+
b^2
4 a^21
x 16.(^2) +^1
2
x+
1
16
=
5
2
+
1
16
c
x a.(^2) +b
a
x=-
c
a
5
x 2.
(^2) +^1
2
x=
5
2
x^2 +b
a
x+c
a
x^2 + = 01
2
x-5
2
= 0
2 x^2 +x- 5 = 0 ax 2 +bx+c= 0 1 a 7022 x^2 +x- 5 = 0ax^2 +bx+c=0.Factor.
Add on
right.NOW TRY
EXERCISE 1
Write the equation in standard
form, if necessary, with 0 on
the right side. Then identify
the values of a, b, and c.
(a)
(b)
(c)
(d) 212 x+ 121 x- 52 =- 3
2 x^2 - 4 x= 0x^2 - 3 =- 2 x3 x^2 - 7 x+ 4 = 0NOW TRY ANSWERS
- (a)
(b)
(c)
(d)a=4, b=-18, c=- 7
a=2, b=-4, c= 0a=1, b=2, c=- 3a=3, b=-7, c= 4Now, identify the required values: a=2,b=1,and c=-5. NOW TRYDetermining Values of a, b, and cin Quadratic Equations
Identify the values of a, b, and cin each quadratic equation
a b c(a)
Here, and a= 2 ,b= 3 , c= - 5.2 x^2 + 3 x- 5 = 0ax^2 +bx+c=0.EXAMPLE 1This equation is in
standard form.Factor.
Add on
right.http://www.ebook777.com
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