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Alg2 lesson 7-5
- 4. Write a polynomial function of least degree with
integer coefficients whose zeros include 2, 1 and -3
x=2 x=1 x = -3
xâ2=0 xâ1=0 x+3=0
(x â 2)(x â 1)(x + 3) = 0
(x2 â 3x + 2)(x + 3) = 0
x3 + 3x2 â 3x2 â 9x + 2x + 6 = 0
x3 â 7x + 6 = 0
- 5. Write a polynomial function of least degree with
integer coefficients whose zeros include 4 and 4 â i.
Complex
x=4 x=4âi x=4+i zeros occur
in
xâ4=0 xâ4+i=0 xâ4âi=0 conjugate
pairs
(x â 4) (x â 4 + i) (x â 4 â i) ïŒ
ïŒ ïŒ ïŒ ïŒ +1
x2 â 4x â xi â 4x + 16 + 4i + xi â 4i â i2
(x â 4) x2 â 8x + 17
- 7. State the possible number of positive real zeros, negative
real zeros, and imaginary zeros of
2 sign changes
+ ï + +
2 or 0 positive zeros
f(-x) = (-x)3 â (-x)2 + 2(-x) + 4
1 sign change
= ï x3 â x2 â 2x + 4 1 negative zero
ï ï ï +
2 or 0 imaginary zeros.
- 8. State the possible number of positive real
zeros, negative real zeros, and imaginary zeros of
2 sign changes
+ ï + + +
2 or 0 positive zeros
p(-x) = (-x)4 â (-x)3 + (-x)2 + (-x) + 3
2 sign changes
= x4 + x3 + x2 - x + 3
2 or 0 negative zeros
+ + + ï +
4, 2, or 0 imaginary zeros.