help solve 2

May 2010
39
0
The polynomial P(x)=x2+ax +b has a zero at x =2. When P(x)is divided by x +1, the remainder is 18.Find the values of a and b.

with working out please
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
The polynomial P(x)=x2+ax +b has a zero at x =2. When P(x)is divided by x +1, the remainder is 18.Find the values of a and b.

with working out please
You have \(\displaystyle P(x) = x^2 + ax + b\).


By the Remainder and Factor Theorems:

If there is a root at \(\displaystyle x = 2\), then \(\displaystyle P(2) = 0\).

If, when you divide by \(\displaystyle x + 1\) you get a remainder of \(\displaystyle 18\), then \(\displaystyle P(-1) = 18\).


So you have:

\(\displaystyle 2^2 + 2a + b = 0\)

\(\displaystyle (-1)^2 - a + b = 18\).


Simplify and solve these equations simultaneously for \(\displaystyle a\) and \(\displaystyle b\).
 
May 2010
39
0
You have \(\displaystyle P(x) = x^2 + ax + b\).


By the Remainder and Factor Theorems:

If there is a root at \(\displaystyle x = 2\), then \(\displaystyle P(2) = 0\).

If, when you divide by \(\displaystyle x + 1\) you get a remainder of \(\displaystyle 18\), then \(\displaystyle P(-1) = 18\).


So you have:

\(\displaystyle 2^2 + 2a + b = 0\)

\(\displaystyle (-1)^2 - a + b = 18\).


Simplify and solve these equations simultaneously for \(\displaystyle a\) and \(\displaystyle b\).
so i get 4+2a+b=0(1) and 1-a+b=18(2)
then i make 1-a+b=18(times by 2) which is 2-2a+2b=36(3)
by elimination method
(3)+(1)
6+3b=36
3b=30
b=10
sub b=10 into (1)
4+2a+10=0
2a=-14
a=-7

is this right?
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
so i get 4+2a+b=0(1) and 1-a+b=18(2)
then i make 1-a+b=18(times by 2) which is 2-2a+2b=36(3)
by elimination method
(3)+(1)
6+3b=36
3b=30
b=10
sub b=10 into (1)
4+2a+10=0
2a=-14
a=-7

is this right?
Yes, well done. (Clapping)
 
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