miraismail2909
Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Find the values of a and b given that the polynomial P(x) = x^3+ ax^2 +x+b, is divisible by
both x-1 and x + 3.​

Sagot :

Answer:

a=4

b=-6

Step-by-step explanation:

If P(x) is divisible by x-c, then P(c)=0.

So P(1)=0 implies 1^3+a1^2+1+b=0

and

P(-3)=0 implies (-3)^2+a(-3)^2+-3+b=0

So notice we have a system to solve.

Let's simply it.

First equation:

1^3+a1^2+1+b=0

1+a+1+b=0

2+a+b=0

a+b=-2

Second equation:

(-3)^3+a(-3)^2+-3+b=0

-27+9a-3+b=0

9a+b-30=0

9a+b=30

Let's put our system together:

a+b=-2

9a+b=30

This is setup so if we subtract the equations b will eliminate allowing us to solve for a:

-8a=-32

a=4

If a=4 and a+b=-2, then 4+b=-2 giving us b=-6.

a=4

b=-6

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.