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# Alg2 lesson 7-5

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• 1. Solve each equation, then state the number and typeof 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 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. 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. Pg. 372
• 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. 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.