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Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

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THE FUNDAMENTAL THEOREM OF ALGEBRA

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Page 1: Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra.

5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

Page 2: Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

HOW MANY SOLUTIONS?

• Can you tell how many solutions a polynomial equation has just by looking at it?

• What are the possible number of solutions to a quadratic equation?

• 2,1, or none

• But this is number of real solutions.• We can tell the number of both real and complex

solutions by using the Fundamental Theorem of Algebra.

Page 3: Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

THE FUNDAMENTAL THEOREM OF ALGEBRA

• If P(x) is a polynomial of degree n≥1, then P(x) = 0 has exactly n roots, include multiple and complex roots.

• Ex: how many roots?

• 5 roots

• What are they?

• 1, 2, -2, i, -i

Page 4: Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

FINDING ALL ZEROS• Find zeros of

• Graph using your calculator

• We see that there are 2 real zeros.

• 3 and -3

• By the Fundamental Theorem of Algebra, there should be two more zeros.

• Use synthetic division to divide by 3 and then divide that quotient by -3

• Find complex roots of

• and these are the other two zeros.

Page 5: Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

PRACTICE

• Using your graphing calculator and the Fundamental Theorem of Algebra, what are the zeros of the function ?

Page 6: Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA

ASSIGNMENT

• Odds p.322 #9-25


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