Candidates were expected to make it clear that the two intersections with the x-axis gave two real roots and, since the polynomial was a quartic and therefore had four zeros, the other two roots must be complex. Candidates who made vague statements such as ‘the graph shows two real roots’ were not given full credit. Rustfeather
To find a polynomial of degree 4 that has the given zeros shown in the graph. Answer to Problem 67E The polynomial of degree 4 that has the given zeros as shown in the graph is,

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Used to Find the Zeros of Polynomials By Masao Igarashi Abstract. A new criterion for terminating iterations when searching for polynomial zeros is described. This method does not depend on the number of digits in the mantissa; moreover, it can be used to determine the accuracy of the resulting zeros. Examples are included. 1. Introduction.

Figure 4: Graph of a third degree polynomial, one intercpet. Answers to Above Questions. Since x = 0 is a repeated zero or zero of multiplicity 3, then the the graph cuts the x axis at one point. An x intercept at x = -2 means that Since x + 2 is a factor of the given polynomial. Hence the given polynomial can be written as: f(x) = (x + 2)(x 2 ...

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Answer to Find all the real and imaginary zeros for each polynomial function.n(x) = 8x3 − 1.

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Finding real roots numerically. The roots of large degree polynomials can in general only be found by numerical methods. If you have a programmable or graphing calculator, it will most likely have a built-in program to find the roots of polynomials. Here is an example, run on the software package Mathematica: Find the roots of the polynomial

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State if the given binomial is a factor of the given polynomial. 26) (55p - p3 - 63p2 + p4 + 2) ... Possible # of imaginary zeros: 4, 2, or 0

The basic idea is that a function with zeros a, b, c, etc is if one of the roots is imaginary

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Factor the polynomial completely. P(x) = x4 + 15x2 − 16 Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary part.)

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( 2 ) Find all the real zeros of the polynomial function. ℎ( )= 2 −6 +9 ( 3 ) Find a polynomial function with the given zeros, multiplicities, and degree.

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2-05 Rational Zeros of Polynomial Functions. Find the rational zeros of 𝑓𝑥=𝑥3−5𝑥2+2𝑥+8 given that 𝑥+1 is a factor. p,q,p/q. Synthetic division. Factor depressed poly. solve-1, 2, 4

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unit 3b - polynomial equations polynomial roots finding rational/irrational roots complex roots sum & difference of cubes imaginary roots writing polynomials given the zeros