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vlada-n [284]
3 years ago
8

1. when the expression x^3+ 2kx+2 is divided by x+2, the remainder is less than the remainder when the expression is divided by

x+1 find the value of k. help plz​
Mathematics
1 answer:
nalin [4]3 years ago
4 0

Answer:

let the polynomial be

f(x)=x³+2kx+2

is divided by

g(x)=x+2

hence

(x+2) is a factor of f(x)

so comparing with x-a we get a=-2

so

f(a)=0

f(-2)=(-2)³+2*-2*k+2

0=-8-4K+2

4k=-6

K=-6/4

k=-3/2

again

when divided by x+1

g(x)=x+1

hence

x+1 is a factor

so a=-1

f(-1)=-(1)³+2*-1*k+2

0=-1-2k+2

0=1-2k

k=1/2

<u>T</u><u>h</u><u>e</u><u> </u><u>v</u><u>a</u><u>l</u><u>u</u><u>e</u><u> </u><u>o</u><u>f</u><u> </u><u>k</u><u> </u><u>i</u><u>s</u><u> </u><u>1</u><u>/</u><u>2</u><u> </u><u>when</u><u> </u><u>divided</u><u> </u><u>by</u><u> </u><u>x</u><u>+</u><u>1</u>

<u>and</u>

<u>K</u><u> </u><u>=</u><u>-</u><u>3</u><u>/</u><u>2</u><u> </u><u>w</u><u>h</u><u>e</u><u>n</u><u> </u><u>d</u><u>i</u><u>v</u><u>i</u><u>d</u><u>e</u><u>d</u><u> </u><u>b</u><u>y</u><u> </u><u>x</u><u>+</u><u>2</u>

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