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Use the resources on the internet and each other to help you relearn the concept. Use whiteboards. Use laptops. Work together.

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We will be reviewing our previous assignment next. So have your questions ready.

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SWBAT write a polynomial function given the real and complex zeros. Write down the date, Section #, Title and Learning Objective(s) into your notebook.

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LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. Complex Number Factoids: Difference of Squares:

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LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. Linear Factorization Theorem If f(x) is a polynomial of degree n where n>0, f has precisely n linear factors. Where c 1, c 2, … c n are complex numbers.

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LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. Linear Factorization Theorem Example This is a second degree polynomial and therefore must have precisely 2 complex zeros. After factoring, we can see that the zero is 3 and is repeated twice. i.e. it has a multiplicity of 2. How would the graph intersect at this zero? How do you know?

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LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. Linear Factorization Theorem Example This is a second degree polynomial and therefore must have precisely 3 complex zeros. After factoring, we can see that the zeros are {0, +2i, -2i}. How many intersection points would the graph have on the x-axis? Why?

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LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. If I am given the zeros, how do I find the polynomial? Take each zero and replace in the Linear Factorization Theorem.

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SWBAT write a polynomial function given the real & complex zeros. LOOK LISTEN Find a 2 nd degree polynomial that has the given zeros of: {-4, 7}.

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Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 3 rd degree polynomial that has the given zeros of: {0, 1, -2}.

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Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 2 nd degree polynomial that has the given zeros of: {-5 with multiplicity of 2}.

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Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 3 rd degree polynomial that has the given zeros of: {0 with multiplicity of 2, -1}.

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LOOK LISTEN SWBAT write a polynomial function given the real & complex zeros. Find a 2 nd degree polynomial that has the given zeros of:. * Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.

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Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 4 th degree polynomial that has the given zeros of:. * Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.

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Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 3 rd degree polynomial that has the given zeros of:. * Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.

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Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 5 th degree polynomial that has the given zeros of:. * Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.

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Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 4 th degree polynomial that has the given zeros of:.

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Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 2 nd degree polynomial that has the given zeros of:.

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Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 4 th degree polynomial that has the given zeros of:.

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Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 4 th degree polynomial that has the given zeros of:.

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Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 2 nd degree polynomial that has the given zeros of:.

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Write a polynomial function with real coefficients that has the given zeros:

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THE LINEAR FACTORIZATION THEOREM. What is the Linear Factorization Theorem? If where n > 1 and a n ≠ 0 then Where c 1, c 2, … c n are complex numbers.

THE LINEAR FACTORIZATION THEOREM. What is the Linear Factorization Theorem? If where n > 1 and a n ≠ 0 then Where c 1, c 2, … c n are complex numbers.

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