Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6...
-
Upload
moses-joseph -
Category
Documents
-
view
216 -
download
0
description
Transcript of Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6...
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.
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
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.
PRACTICE
• Using your graphing calculator and the Fundamental Theorem of Algebra, what are the zeros of the function ?
ASSIGNMENT
• Odds p.322 #9-25