The author wants you to FOIL! STOP! TOO MUCH WORK! Alternative, less work! Combine both complex...
5
4 x 1 x 1 x i x 4 i x 4 0 1 x 0 1 x 0 4 i x 0 4 i x 0 4 4 1 1 i x i x x x The author wants you to FOIL! 1 2 2 x x STOP! TOO MUCH WORK! i x 4 Alternative, less work! Combine both complex zeros with + sign. 0 4 4 16 4 4 2 2 i i ix i x ix x x Isolate the i term. i x 4 Square both sides. 2 2 4 i x 1 16 8 2 x x 0 17 8 2 x x 2 2 1 x x 0 17 8 2 x x
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Transcript of The author wants you to FOIL! STOP! TOO MUCH WORK! Alternative, less work! Combine both complex...
4x
1x 1x ix 4 ix 401x 01x 04 ix 04 ix 04411 ixixxxThe author wants you to FOIL!
122 xx
STOP! TOO MUCH WORK!
ix 4
Alternative, less work!Combine both complex zeros with + sign.
0441644 22 iiixixixxxIsolate the i term.
ix 4Square both sides.
224 ix 11682 xx
01782 xx
2 2 1x x 01782 xx
Multiply 122 xx 01782 xx
122 xx
1782 xx
173417 2 xxxxx 8168 23
234 2 xxx
172626 234 xxxx xf
Find the zeros of 18452553 234 xxxxxf . Rewrite f(x) in linear factored form.
Zeros at x = -2
x = 1/3
The next zero is a fraction between 0 and 1. The rational zero test gives us 1/3 or 2/3. Try 1/3.
We have two rational zeros and time to factor them out to a quadratic function.
Find the zeros of 18452553 234 xxxxxf . Rewrite f(x) in linear factored form.
Zeros at x = -2 x = 1/33 5 25 45 -18
-2 3 -1
-6
27
2
-9
-54 18
0
1/3 3 0
1
27
0
0
9
Solve for x.23 27 0x 2 9 0x 2 9
9
3
x
x
x i
x = + 3i
Factored form.( x + 2 ) ( 3x – 1 ) ( x + 3i ) ( x – 3i )
Find the zeros of . Given one of the zeros is x = 3 + 2i 13463610 234 xxxxxf
1 -10 36 -46 -13
3 + 2i 1
3 + 2i
0
1 - 4 -1 0Go to MODE and turn on a + bi
-7 + 2i
-25 – 8i
11 – 8i
49 – 2i
3 – 2i
13
3 – 2i
3 – 2i -12 + 8i -3 + 2i
0142 xx Complete the square.
___1___42 xx
4124 22 xx
52 2 x
52 x
52 x ix
x
23
52
