In the set of polynomials in the form: P(x) = ax + bx' + cx² + dx + e, x E R there is a subset M, which consists of polynomials whose graph intersect all the coordinates ( -2, 4), (-1, 0), (1,-2), (3, 6). 4 (a) Does M have ploynomials of lower degree than 4, if yes, specify which.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.1: Polynomials Over A Ring
Problem 12E: a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant...
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In the set of polynomials in the form:
4
P(x)
there is a subset M, which consists of polynomials whose graph
intersect all the coordinates (-2, 4), ( -1, 0), (1,-2), (3, 6).
= ax" + bx + cx + dx + e, x E R
(a) Does M have ploynomials of lower degree than 4, if yes,
specify which.
(b) Arrange the coefficients {a, b, c, d, e} for polynomials in M
in parametric form.
(c) Specify the two polynomials in M whose tangents in the
coordinate (1,-2) are orthogonal.
Transcribed Image Text:In the set of polynomials in the form: 4 P(x) there is a subset M, which consists of polynomials whose graph intersect all the coordinates (-2, 4), ( -1, 0), (1,-2), (3, 6). = ax" + bx + cx + dx + e, x E R (a) Does M have ploynomials of lower degree than 4, if yes, specify which. (b) Arrange the coefficients {a, b, c, d, e} for polynomials in M in parametric form. (c) Specify the two polynomials in M whose tangents in the coordinate (1,-2) are orthogonal.
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