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6.7 Using the Fundamental Theorem of Algebra When all real and imaginary solutions are counted, a polynomial of degree n has exactly n solutions when you count both the real and imaginary solutions. Quadratic Equations: Degree =_____________ Find ALL zeroes of the equations below: 1.) y = x 2 − 4 2.) y = x 2 + 4 Solutions:________ 3.) Solutions:___________ y = x2 − 2x + 1 Solutions: _____________ Special Case Called_________ Quadratic Equations will always have a total of ________ real and imaginary solutions. Cubic Equations: Degree = _______________ Find all zeroes of the equations below: 1.) y = x 3 − x 2 − 2 x Solutions: ______________ 2.) y = x 3 + 3 x 2 + 16 x + 48 Solutions:______________ 3.) y = x 3 + x 2 − x + 15 Solutions: ____________ 6.7 Using the Fundamental Theorem of Algebra Cubic Equations will always have a total of ________ real and imaginary solutions. Quartic Equations Degree=___________ Find all zeroes of the equations below: 1.) y = x 4 + 5 x 3 + 5 x 2 − 5 x − 6 Solutions:____________ 2.) y = x 4 − x 3 + 2 x 2 − 4 x − 8 Solutions:_____________ 3.) y = x 4 + x 2 − 12 Solutions:_______________ Quartic Equations will always have a total of ________ real and imaginary solutions. 6.7 Using the Fundamental Theorem of Algebra Quintic Equations Degree:___________ y = x 5 − 2 x 4 + 8 x 2 − 13 x + 6 Quintic Equations will always have a total of ________ real and imaginary solutions. Write the polynomial function of the least degree that has real coefficients, the given zeroes and a leading coefficient of 1. 1.) -6,3,5 2.) 2,-2,-6i 3.) 5, 2+3i 6.7 Using the Fundamental Theorem of Algebra Homework: p. 369 #22-46 even