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Notes Day 6.2

Notes Day 6.2. Irrational Root Theorem Imaginary Root Theorem Factors and their multiplicity Find relative max/min on the graphing calculator. Notes 6.2 Irrational Root Theorem. If is an S / R / Z / x-intercept, then the conjugate

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Notes Day 6.2

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  1. Notes Day 6.2 Irrational Root Theorem Imaginary Root Theorem Factors and their multiplicity Find relative max/min on the graphing calculator

  2. Notes 6.2 Irrational Root Theorem If is an S / R / Z / x-intercept, then the conjugate __________ must ALSO be an S / R / Z / x-intercept EXAMPLE A polynomial equation with integer coefficients has 4 roots. If two of them are and , what are the other two? __________________ and _________________

  3. Write a quartic Polynomial equation that has zeros at 1, -1, and

  4. Imaginary Root Theorem If a + bi is an S / R / Z / x-intercept, then the conjugate __________ must ALSO be an S / R / Z / x-intercept EXAMPLE A polynomial equation with integer coefficients has 4 roots. If two of them are 3 – i and 2i , what are the other two? ______________________ and _____________________

  5. Write a cubic Polynomial equation that has zeros at 2 and 4+i ix -4x x2 -8x2 17x x3 -4x 16 -4i -ix 4i -2x2 16x -i2 -34

  6. Multiplicity The number of times an S / R / Z / x-intercept is ___________________ in a given polynomial equation. REPEATED EXAMPLES: name the root(s) and multiplicity y = x(x2 – 4x + 4) y = x(x-2)(x-2) Once 2 Once -1 0 Once 2 Twice Twice -4

  7. Solve the equation! The square root method works since no linear term x2+ 4 = 0 x2 = – 4

  8. Solve the equation!

  9. Solve the equation!

  10. Factor to find roots but use calculator to find relative min/max. y = 2x3 + 14x2 – 3x – 21 y-int = -21

  11. Factor to find roots but use calculator to find relative min/max. y = 3x5 + 18x4 + 27x3 Work this on back of your notes! Local minimum is: -25

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