Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
The polynomial of 3rd degree whose zeros and degree are given as for zero of (-2), multiplicity 1 and for zero of (3), multiplicity 2 is [tex]f(x)=(x^{3}-10x^{2} -15x+18)[/tex]
As per the question statement, a 3rd degree polynomial has a zero of (-2), multiplicity 1 and another zero of (3), multiplicity 2.
We are required to determine the polynomial.
Since, (-2) is a zero of the polynomial, then [tex][x-(-2)]=(x+2)[/tex] will be a factor of the polynomial. And since for zero of (-2), multiplicity is 1, this means that the factor of (x + 2) is only multiplied once.
Similarly, as (3) is another zero of the polynomial, then [tex](x-3)[/tex] will be a factor of the polynomial. And since for zero of (3), multiplicity is 2, this means that the factor of (x - 3) will be multiplied twice, i.e., [tex](x-3)^{2}[/tex].
Therefore, our function, say, f(x) will be [tex](x+2)(x-3)^2[/tex]
[tex]or, f(x) = (x+2)(x-3)^2\\or, f(x) = (x + 2)(x^{2} +9-12x)\\or,f(x) =x^{3}+9x-12x^{2} +2x^{2} +18-24x\\ or, f(x)=x^{3}+(2x^{2}-12x^{2})+(9x-24x)+18\\or, f(x)=(x^{3}-10x^{2} -15x+18)[/tex]
Hence, our required polynomial is [tex]f(x)=(x^{3}-10x^{2} -15x+18)[/tex]
- Polynomial: A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)
- Degree of a Polynomial: The highest value of power of the variable of a polynomial is known as the degree of the polynomial.
- Zero of a Polynomial: The value of the variable for which, the polynomial or equation equates to zero, is known as Zero of the Polynomial.
To learn more about Polynomials, Degrees and Zeroes, click on the link below.
https://brainly.com/question/2272957
#SPJ9
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
