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Form a polynomial whose zeros and degree are given. Zeros: 4, multiplicity 1; -3, multiplicity 2; Degree:3

source : algebra.com

Form a polynomial whose zeros and degree are given. Zeros: 4, multiplicity 1; -3, multiplicity 2; Degree:3

SOLUTION: Form a polynomial whose zeros and degree are given.
Zeros: 4, multiplicity 1; -3, multiplicity 2; Degree:3

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Question 1164186: Form a polynomial whose zeros and degree are given.Zeros: 4, multiplicity 1; -3, multiplicity 2; Degree:3
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Found 2 solutions by Edwin McCravy, AnlytcPhil:Answer by Edwin McCravy(18569)   (Show Source):
You can put this solution on YOUR website!
I won’t do yours for you, but I’ll do one exactly like yours
that you can use as a model to do yours by:
Zeros: 5, multiplicity 1; -4, multiplicity 2; Degree:3

So write x = 5 once, x = -4 twice

x = 5; x = -4; x = -4

Get 0 on the right of each of the three equations:

x – 5 = 0 x + 4 = 0 x + 4 = 0

Multiply all three left sides together and set it equal to what you get
when you multiply all three right sides together, 0∙0∙0 = 0

(x – 5)(x + 4)(x + 4) = 0

Then you multiply that out

(x² + 4x – 5x – 20)(x + 4) = 0

(x² – x – 20)(x + 4) = 0

x³ + 4x² – x² – 4x – 20x – 80 = 0

x³ – 3x² – 24x – 80 = 0

The polynomial that has the given zeros is the polynomial
that when set equal to 0 has those solutions, so the
polynomial that when set equal to zero is the polynomial
that’s set equal to 0 above, which is this polynomial,
which we’ll call P(x):

P(x) = x³ – 3x² – 24x – 80

Answer by AnlytcPhil(1758)   (Show Source):

Form a Polynomial given the Degree and Zeros | math15fun.com

Form a Polynomial given the Degree and Zeros | math15fun.com – Solution: By the Fundamental Theorem of Algebra, since the degree of the polynomial is 4 the polynomial has 4 zeros if you count multiplicity. There are three given zeros of -2-3i, 5, 5. The remaining zero can be found using the Conjugate Pairs Theorem. f (x) is a polynomial with real coefficients.About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us CreatorsFind an answer to your question "Form a polynomial whose zeros and degree are given Zeros: – 9, multiplicity 1; – 1, multiplicity 2; degree 3" in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.

Finding a polynomial of a given degree with given zeros – A polynomial of degree 3 has 3 zeros, and you are given the three zeros, they are -2, -2 and 4. If a polynomial of degree 3 has roots a, b and c, it's factorised form is k(x-a)(x-b)(x-c) = 0. But we can say that k = 1 since we don't have any points it needs to go through, and substituting in the given zeros tells us its factorised form isForm a polynomial whose zeros and degree are given. Zeros: 3, multiplicity 1; 2, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.show help ↓↓examples ↓↓. INSTRUCTIONS: 1 . This calculator will generate a polynomial from the roots entered below. 2 . You can input integers (10), decimals (10.2) and fractions (10/3). 3 . Roots need to be separated by comma. 0123456789-/.,del.

Finding a polynomial of a given degree with given zeros

Form a polynomial whose zeros and degree are given Zeros – Polynomial function is x^3-3x^2-4x+12 A polynomial function whose zeros are alpha, beta, gamma and delta and multiplicities are p, q, r and s respectively is (x-alpha)^p(x-beta)^q(x-gamma)^r(x-delta)^s It is apparent that the highest degree of such a polynomial would be p+q+r+s. As zeros are -2, 2 and 3 and degree is 3, it is obvious that multiplicity of each zero is just 1.If a polynomial P (x) has a zero equal to a, then (x-a) is a factor of this polynomial. So if a polynomial has zeros a, b and c then it has we could write: P (x)= (x-a) (x-b) (x-c). Here we can clearly see that a, making the left hand side 0 because of the factor (x-a), makes the left hand side 0 as well.Question 1146421: Form a polynomial whose zeros and degree are given. Zeros: -4, multiplicity 1; -3, multiplicity 2; degree 3. Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. Found 2 solutions by richwmiller, josgarithmetic: Answer by richwmiller (17219) ( Show Source ):

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