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Alg2 lesson 7-5
1.
Solve each equation,
then state the number and type of roots. one real root two real roots
2.
one real root
and two imaginary roots
3.
two real roots
and two imaginary roots
4.
Write a polynomial
function of least degree with integer coefficients whose zeros include 2, 1 and -3 x=2 x=1 x = -3 x–2=0 x–1=0 x+3=0 (x – 2)(x – 1)(x + 3) = 0 (x2 – 3x + 2)(x + 3) = 0 x3 + 3x2 – 3x2 – 9x + 2x + 6 = 0 x3 – 7x + 6 = 0
5.
Write a polynomial
function of least degree with integer coefficients whose zeros include 4 and 4 – i. Complex x=4 x=4–i x=4+i zeros occur in x–4=0 x–4+i=0 x–4–i=0 conjugate pairs (x – 4) (x – 4 + i) (x – 4 – i) +1 x2 – 4x – xi – 4x + 16 + 4i + xi – 4i – i2 (x – 4) x2 – 8x + 17
6.
Pg. 372
7.
State the possible
number of positive real zeros, negative real zeros, and imaginary zeros of 2 sign changes + + + 2 or 0 positive zeros f(-x) = (-x)3 – (-x)2 + 2(-x) + 4 1 sign change = x3 – x2 – 2x + 4 1 negative zero + 2 or 0 imaginary zeros.
8.
State the possible
number of positive real zeros, negative real zeros, and imaginary zeros of 2 sign changes + + + + 2 or 0 positive zeros p(-x) = (-x)4 – (-x)3 + (-x)2 + (-x) + 3 2 sign changes = x4 + x3 + x2 - x + 3 2 or 0 negative zeros + + + + 4, 2, or 0 imaginary zeros.