Question

Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x) bounces off of the x-axis at 5, breaks through the x-axis at −1, has complex roots of −5−3i and −4+2i and passes through the point (0,89).

Answer #1

Find an equation for f(x), the polynomial of smallest degree
with real coefficients such that f(x) breaks through the x-axis at
−5, breaks through the x-axis at −4, has complex roots of 5−i and
−3−5i and passes through the point (0,68).

Form a polynomial f(x) with the real coefficients having the given
degree and zeros
Degree 4; zeros: -1,2 and 1-2i

Form a polynomial f(x) with real coefficients having the given
degree and zeros.
Degree 4;
zeros:-5+3i, -4 multiplicity 2
please show all steps and explain

in exercises 47-50, find the polynomial function f with real
coefficients that has the given degree, zeros, and solution point.
degree 3. zeros -3, 1+ square root 3i. solution point f(-2)=12

form a polynomial F(x) with real coefficients having the given
degree and zeros
degree 4
zeros 2-3i; -3 multiplicity 2

Let f(x) be a cubic polynomial of the form x^3 +ax^2 +bx+c with
real coefficients.
1. Deduce that either f(x) factors in R[x] as the product of
three degree-one
polynomials, or f(x) factors in R[x] as the product of a
degree-one
polynomial and an irreducible degree-two polynomial.
2.Deduce that either f(x) has three real roots (counting
multiplicities) or
f(x) has one real root and two non-real (complex) roots that are
complex
conjugates of each other.

Find a polynomial f (x) of degree 4 with real coefficients and
the following zeros.
4 (multiplicity 2) , i
f(x)=

Find a polynomial P(x) with real coefficients having a degree
4, leading coefficient 4, and zeros 2-i and 3i.

Find the polynomial with real coefficients of the smallest possible
degree for which 4i and 1+i are zeros and in which the coefficient
of the highest power is 1.

1. Find a polynomial equation with real coefficients that has
given zeros.
3 - 7i and 3 + 7i
The equation is x2 - ___x + ___ = 0
2. Find all complex zeros of the polynomial function. Give exact
values. List multiple zeros as necessary.
f(x) = x4 +10x3 - 31x2 + 80x -
312
All complex zeros are ____
3. Find all complex zeros of the polynomial function. Give exact
values. List multiple zeros as necessary.
f(x) =...

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