notes over 6.7 finding the number of solutions or zeros find the number of zeros of the polynomial...
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Notes Over 6.7Finding the Number of Solutions or Zeros
2 .1 234 xxxxxfFind the number of zeros of the polynomial function.
12198 .2 23 xxxxf
Notes Over 6.7Finding the Number of Solutions or Zeros
1052 .3 23 xxxxfFind the number of zeros of the polynomial function.
xxxxxf 1243 .4 234
Notes Over 6.7Finding the Zeros of a Polynomial Function
2 .5 234 xxxxxfFind all the zeros of the polynomial function.
1 1 1 1 11
22 1 2
1
1
q
p ,1 2
1 1
12
00 1 0
2
2
22
22x 01
12 xix 1x
21
2 01
2x
Notes Over 6.7Finding the Zeros of a Polynomial Function
12198 .6 23 xxxxfFind all the zeros of the polynomial function.
1 1 8 19 121
7 7 12 0
1
12
q
p ,1 2
11
2x x7
3x 4x 1x
,3 ,4,6 ,12
1012
0 x x3 4
Notes Over 6.7Finding the Zeros of a Polynomial Function
1052 .7 23 xxxxfFind all the zeros of the polynomial function.
2 1 2 5 101
00 5 0
2
10
q
p ,1 2
22
2x
,5 10
205 52 x
5ix 2x
Notes Over 6.7Finding the Zeros of a Polynomial Function
xxxxxf 1243 .8 234 Find all the zeros of the polynomial function.
2 1 3 4 121
510 6 0
2
12
q
p ,1 ,2
22
22x x5
1243 23 xxxx ,3 ,4,6 ,12
06 x x3 2
3x2x
2x0x
x
Notes Over 6.7Using Zeros to Write Polynomial Functions
5 1, 2, .9
Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.
2x2x x 2
25 2 xxx3x x22x
25x 3xxf 26x x3
1x 5xx2
x5 1010
Notes Over 6.7Using Zeros to Write Polynomial Functions
6 3, 4, .10
Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.
4x2x x3 12
126 2 xxx3x x122x
26x 3xxf 27x x6
3x 6xx4
x6 7272
Notes Over 6.7Using Zeros to Write Polynomial Functions
7 1, ,1 .11
Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.
1x2x x 1
17 2 xx3x 27xx
3xxf 27x x
1x 7xx
7
7
Notes Over 6.7Using Zeros to Write Polynomial Functions
2 ,3 ,3 .12
Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.
3x2x x3 9
92 2 xx3x 22xx9
3xxf 22x x9
3x 2xx3
18
18
Notes Over 6.7Approximating Real Zeros
26 .13 3 xxxf
Use a graphing calculator to graph the polynomial function. Then use the Zero (or Root) feature of the calculator to find the real zeros of the function.
x-inter: -2.6, 0.3, 2.26
Notes Over 6.7Approximating Real Zeros
1 .14 23 xxxxf
Use a graphing calculator to graph the polynomial function. Then use the Zero (or Root) feature of the calculator to find the real zeros of the function.
x-inter: 1
Notes Over 6.7Approximating Real Zeros
343 .15 23 xxxxf
Use a graphing calculator to graph the polynomial function. Then use the Zero (or Root) feature of the calculator to find the real zeros of the function.
x-inter: -0.52
Notes Over 6.7Approximating Real Zeros
13 .16 3 xxxf
Use a graphing calculator to graph the polynomial function. Then use the Zero (or Root) feature of the calculator to find the real zeros of the function.
x-inter: -1.53, -0.35, 1.88
Notes Over 6.7