Question

The cubic polynomial P(x) = x3 + bx2 + cx + d (where b, c, d are real numbers) has three real zeros: -1, α and -α.

(a) Find the value of b

(b) Find the value of c – d

Answer #1

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local
maximum value of 4 at x = −2 and a local minimum value of 0 at x =
1.

. For the quartic function f(x) = ax4 + bx2 + cx + d, find the
values of a, b, c, d such that there is a local maximum at (0, -6)
and a local minimum at (1, -8). How do you find this?

1) find a cubic polynomial with only one root
f(x)=ax^3+bx^2+cx +d such that it had a two cycle using Newton’s
method where N(0)=2 and N(2)=0
2) the function G(x)=x^2+k for k>0 must ha e a two cycle
for Newton’s method (why)? Find the two cycle

Use a system of equations to find the cubic function
f(x) = ax3 + bx2 + cx + d
that satisfies the equations. Solve the system using
matrices.
f(−1) = 10
f(1) = 8
f(2) = 34
f(3) = 94

A20) Given that f(x) is a cubic function with
zeros at −2−2 and 2i−2, find an equation for f(x) given that
f(−7)=−6
B19) Find a degree 3 polynomial whose coefficient
of x^3 equal to 1. The zeros of this polynomial are 5, −5i, and 5i.
Simplify your answer so that it has only real numbers as
coefficients.
C21) Find all of the zeros of P(x)=x^5+2x^3+xand
list them below with zeros repeated according to their
multiplicity.
Note: Enter the zeros as...

Question 1a Consider the polynomial function P(x) = x3+x2−20x.
Sketch a graph of y = P(x) by: determining the zeros of P(x),
identifying the y-intercept of y = P(x), using test points to
examine the sign of P(x) to either side of each zero and deducing
the end behaviour of the polynomial.
b Consider the quadratic function f(x) = 2x2 + 8x−1. (a) Express
f(x) in standard form. (b) Determine the vertex of f(x). (c)
Determine the x- and y-intercepts...

Suppose that f(x)=ax^3+bx^2+cx+d cubic polynomial.. Show that
f(x) and k(x)=f(x-2) have the same number of roots.(without
quadratic formula)

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.

1. A zero of a polynomial p(x) ∈ R[x] is an element α ∈ R such
that p(α) = 0. Prove or disprove: There exists a polynomial p(x) ∈
Z6[x] of degree n with more than n distinct zeros.
2. Consider the subgroup H = {1, 11} of U(20) = {1, 3, 7, 9, 11,
13, 17, 19}.
(a) List the (left) cosets of H in U(20)
(b) Why is H normal?
(c) Write the Cayley table for U(20)/H.
(d)...

the linear transformation, L(p(x))=d/dx p(x)+p(0). maps a
polynomial p(x) of degree<= 2 into a polynomial of degree
<=1, namely, L:p2 ~p1. find the marix representation of L with
respect to the order bases{x^2,x,1}and {x,1}

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 6 minutes ago

asked 7 minutes ago

asked 11 minutes ago

asked 13 minutes ago

asked 13 minutes ago

asked 22 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 45 minutes ago

asked 53 minutes ago

asked 54 minutes ago