Alg2 lesson 7-5

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Alg2 lesson 7-5

  1. 1. Solve each equation, then state the number and typeof roots. one real root two real roots
  2. 2. one real root and two imaginary roots
  3. 3. two real roots and two imaginary roots
  4. 4. Write a polynomial function of least degree withinteger 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. 5. Write a polynomial function of least degree withinteger 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. 6. Pg. 372
  7. 7. State the possible number of positive real zeros, negativereal 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. 8. State the possible number of positive realzeros, 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.

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