The polynomial of degree 3, P(x), has a root of multiplicity 2 at r = 1 and a root of multiplicity 1 atx = - 3. The y-intercept is y = - 1.5.Find an equation for P(x).P(x) =

Answered: The polynomial of degree 3, P(x), has a…

The polynomial of degree 3, P(x), has a root of multiplicity 2 at a = 1 and a root of multiplicity 1 at x = - 3. The y-intercept is y Find an equation for P(x). - 1.5. P(x) =

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.5: Complex Zeros And The Fundamental Theorem Of Algebra

Problem 3E: A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is...

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Question

The polynomial of degree 3, P(x), has a root of multiplicity 2 at r = 1 and a root of multiplicity 1 at
x = - 3. The y-intercept is y = - 1.5.
Find an equation for P(x).
P(x) =

Expert Solution

Step 1

$s o l u t i o n : - r o o t x = 1, m u l t i p l i c i t y = 2 r o o t x = - 3, m u l t i p l i c i t y = 1 y - i n t e r c e p t (a t x = 0) = - 1.5 t h e e q u a t i o n o f 3 d e g r e e p o l y n o m i a l P (x) i s g i v e n b y P (x) = a {(x - 1)}^{2} (x + 3) w h e r e a i s c o n s \tan t$

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