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About featured snippets•FeedbackQuestions & answersSocraticQuestionHow do you write a polynomial function with the given zeros 1, –2, and 5?Answer · 0 votesx3−4x2−7x+10Explanation:A polynomial with a zero at x=a has a factor (x−a), so the required polynomial is: (x−1)(x+2)(x−5)=(x2+x−2)(x−5)=x3−4x2−7x+10MoreWyzantQuestionWriting polynomial functions with complex zerosAnswer · 3 votesSince the polynomial has rational coefficients, complex roots occur in conjugate pairs, so, since 4 + i is a root, 4 - i must be a root as well.By the Factor Theorem, if c is a root of f(x), then x - c is a factor of f(x).Therefore, the polynomial with smallest possible degree and with leading coefficient 1 would be:(x - 5)(x - 5)(x - (4 + i))(x - (4 - i))= (x2 - 10x + 25)((x - 4) - i)((x - 4) + i)= (x2 - 10x + 25)((x - 4)2 - i2)= (x2 - 10x + 25)(x2 - 8x + 16 + 1)= (x2 - 10x + 25)(x2 - 8x + 17)= X4 - 8X3 + 17X2 -10X3 + 80X2 - 170X + 25X2 - 200X + 425= X4 -18X3 +122X2 - 370X + 425MoreSocraticQuestionHow do you write a polynomial function with the given zeros 2 and 2i and degree 3?Answer · 0 votesYou need to write three factors: (x−2)(x−2i)(x+2i) based on the Factor Theorem and Complex Conjugates Theorem.Explanation:Now, expand the expression: (x−2)(x2+4)=x3−2x2−4x−8Notice that the polynomial is of degree 3, called a "cubic".Observe that the graph of the function only has one "zero" at 2. That is because the other two algebraic zeros are imaginary numbers, 2i and -2i, which can not be plotted on the real number coordinate plane:my screenshot 3MoreStudy.comQuestionWrite the simplest polynomial function with the given zeros. a) 1/3, 1, 2 b) -2, 2, 3Answer · 0 votesa)A polynomial with roots13,1,2will bef(x)=(x−13)(x−1)(x−2)=(x2−43x+13)(x−2)=x3−43x2+13x−2x2+43x−23=x3−103x2+53x−23b)A polynomial with roots−2,2,3will bef(x)=(x+2)(x−2)(x−3)=(x2−4)(x−3)=(x2−4)x−3(x2−4)=x3−4x−3x2+12=x3−3x2−4x+12c)A polynomial with roots−2,12,2will bef(x)=(x+2)(x−2)(x−12)=(x2−4)(x−12)=(x2−4)x−12(x2−4)=x3−4x−12x2+2=x3−12x2−4x+2MoreStudy.comQuestionHow to find a polynomial function with given zeros with imaginary numbers?Answer · 0 votesIf you know how to multiply binomials and other polynomials, then you know how to find a polynomial function given the zeros. Here are the steps you would follow.1. Take the given roots and write them as a factor of the polynomial. For example, if our roots were 2,−1,3i,−3i, we would write the factors for our function P as P(x)=(x−2)(x+1)(x−3i)(x+3i). Note that the root of 2 gave us the factor of (x−2).2. Now you multiply the factors together. It will be easier if you multiply the imaginary factors first. You can use the acronym FOIL or another multiplication method to do this.When we multiply the imaginary factors, we get (x−3i)(x+3i)=x2+3ix−3ix−9i2=x2+9.Did you see how the imaginary terms canceled each other out? Also remember that we were able to make −9i2=9 since i2=−1.If we multiply the other two factors, we get that (x−2)(x+1)=x2+x−2x−2=x2−x−2. So now we have P(x)=(x2−x−2)(x2+9).3. Keep multiplying the factors together. To multiply the trinomial by the binomial, we mu…MoreStack ExchangeQuestionPolynomial Function given roots and a pointAnswer · 2 votesTo elaborate on SmileyCraft's answer (they give the answer but not the underlying reason why, which I feel is more important).The Roots:On first contending with the roots issue, which the comments hint you had trouble with: we know −2i and 5 are roots. We know that since −2i is a root, +2i is also a root because it's the conjugate of −2i. Then, since 5,−2i,+2i are all roots, we know that the polynomial can be factored asf(x)=a(x−5)(x−2i)(x+2i)up to a leading coefficient a that I'll talk about later. (You assumed a=1, and I'll explain why that's wrong in the next section.) It should be clear that this form is correct otherwise, since plugging in any of our roots gives f(x)=0.Since you wanted real coefficients and such, we note that (x−2i)(x+2i)=x2+4, thus giving us the form you posed in the question (again, up to that constant a).Finding a:So now you know that the polynomial has the formf(x)=a(x−5)(x2+4)The reason we include this a is because the leading coefficient …MoreNumeradeQuestionWrite a polynomial function in standard form with the given zeros. -1,2,5Answer · 2 votesHello, everybody. Welcome. We want to write a point Normal function in standard form with the given zeros, X is equal to negative one, two and five. And when writing a polynomial function on and we want a first, write it in factored form and then we can later converted into its standard form. So we have F f X is equal to and are factors are going to be expressions for which ex will evaluate to zero, so we have X plus one X minus two and X minus five. Now the reason I chose these three factors was because when you plug in any one of these three values into X, uh, it would evaluate zero. For example, if I plugged in five, uh, this expression right over here would become zero and anything Times zero is zero. So therefore the succession would be zero, and that is the definition off X intercept. It's when Why? Why is equal to zero? So now that we haven't infected form, it's simply just a matter of converting it into a standard form. And the way we can do that is by expanding our 1st 2 terms…MoreQuoraQuestionHow do you write a polynomial function using the linear factors associated with the given zeros (X= {+- 2, 3+I, 0 (multiplicity of 2), +- 2 square root of 3)?Answer · 0 votesThe factor for a root of zero (twice) is x^2.The factor for roots of +-2 is x^2–4.The factor for roots of +- 2 square root of 3 is x^2–12.The factor for a root of 3+i implies another root 3-i and it comes from(x-3)^2 = -1 (roots 3+i and 3-i) factor (x^2–6x+10)MoreStack ExchangeQuestionI've been having trouble with this problem: Find a polynomial function of minimum degree with −1 and 1−√3 as zeros. Function must have integer coefficients.When I tried it, I got this:(x+1)(x−(1−√3))=x2−x(1−√3)+x−1+√3=x2−x+x(√3)+x−1+√3=x2+x(√3)−1+√3This looks completely wrong to me and it probably is as my teacher said the answer should not be a quadratic. I'm not looking for the answer to be given to me; but if I could get some guidance, it would be greatly appreciated.Answer · 1 voteYour polynomial does not work because it does not have integer coefficients. So no quadratic will work, because the two roots are forced to be −1 and 1−√3, and you just showed this doesn't work.However, a cubic will work. Try the one with −1, 1−√3, and 1+√3 as roots.MoreBrainly.comQuestionWrite a polynomial function with the given zeros. multiply the terms (write in standard form). 1) x= -1, -1, 2 2) x= -2, 0, 3Answer · 0 votes[tex]1) f(x)=x^3-3x-2 2) g(x)=x^3-x^2-6x[/tex] Explanation: [tex]A mathbf{polynomial function} of x with degree n is given by: f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+ldots +a_{2}x^{2}+a_{1}x+a_{0} where n is a nonnegative integer and a_{n}, a_{n-1}, ldots a_{2}, a_{1}, a_{0} with a_{n}eq 0[/tex] In this exercise, we have two cases and both will be polynomial functions with degree 3 because we have three real roots in each case. So: First. The roots are: [tex]x= -1, -1, 2[/tex] So we can write this polynomial functions as the product of linear factors: [tex]f(x)=(x-(-1))(x-(-1))(x-2) f(x)=(x+1)^2(x-2)[/tex] Since we have to write it in standard form, let's expand: [tex]f(x)=(x+1)^2(x-2) By property: (a+b)^2=a^2+2ab+b^2 f(x)=(x^2+2x+1)(x-2) f(x)=x^3+2x^2+x-2x^2-4x-2 Combine like terms: x^3+(2x^2-2x^2)+(x-4x)-2 boxed{f(x)=x^3-3x-2}[/tex] Second. The roots are: [tex] x= -2, 0, 3[/tex] Writing th…MoreBartleby.comQuestionWrite a polynomial function in standard form with the given zeros. (show work)x = -1, 5, -2Answer · 0 votesStep 1 Given : the zeros are x=-1, 5 -2Let p(x) be the polynomial function in the standard formdefined by p(x)=k(x-a)(x-b)(x-c); where x=a,b,c are the zeros of p(x) .MoreCheggQuestionWrite a polynomial function with the given zeros and their corresponding multiplicities. There are many possible answers. Zeros Mult. 2 3 1 1 3 -3 g(x) Write a polynomial function with the given zeros and their corresponding multiplicities. There are many possible answers. Zeros Mult. 0 3 -1 2 3 2 f(x) =Answer · 0 votes1. Given a following zeros and multiplicity table:MoreQuizletQuestionWrite a polynomial function in standard form with the given zeros.x=1, -1, -2Answer · 0 votesBy the Zero Product Property, if one of the factors of an expression is equal to zero, then the expression is equivalent to zero. So, given each solution, $a$, we can find a factor $(x-a)$ of the polynomial and then multiply the factors to get the polynomial.$$x=1quad Rightarrow quad text{Factor: } color{#c34632}{(x-1)}$$$$x=-1quad Rightarrow quad text{Factor: } color{#c34632}{(x+1)}$$$$x=-2quad Rightarrow quad text{Factor: } color{#c34632}{(x+2)}$$Now, multiply each of these factors together to get the polynomial.$$begin{align*}color{#4257b2}{(x-1)(x+1)}color{default}(x+2)&=left[color{#4257b2}{underbrace{(x)(x)}_{color{#c34632}{text{First. More resultsWhat is the root of a polynomial?The roots of a polynomial are those values of the variable that cause the polynomial to evaluate to zero. Kay Jewelers Chambersburg Pa, How to Find the Real Roots of a Polynomial Using Descartes's Rule .. More results Feedback People also askYou will see more English now.How to write a polynomial function with given zeros and degree?How to write a polynomial function with given zeros and multiplicity?How to write a polynomial function with given zeros and imaginary numbers?How to write a polynomial function with given zeros and leading coefficient?FeedbackVideosYou will see more English now.4:19Write the equation of the polynomial given the zerosYouTube · Brian McLogan4 minutes, 19 secondsAug 16, 20133 key moments in this videoFrom 00:00IntroFrom 00:35Start of ProblemFrom 03:09Made a mistake. -3 times x, was supposed to be -3x, not just 3x3:52Write the equation of the polynomial given the zerosYouTube · Brian McLogan3 minutes, 52 secondsSep 18, 20126 key moments in this video3:38Write the equation of the polynomial given the zerosYouTube · Brian McLogan3 minutes, 38 secondsSep 18, 20123 key moments in this videoFeedbackView all Kay Jewelers Chesterfield Towne Center, How to Find a Polynomial of a Given Degree . - Study.com. 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