Using remainder theorem, find the value of ‘a’ if the division of x³ +5x² -ax+6 by (x-1) leaves the remainder 2.
Answers
Answered by
4
Answer:
10
Step-by-step explanation:
Let P(x)=x³ +5x²-ax+6
Zero of x-1 =0
=>x =1
P(1)=(1)³+5(1)² -a(1)+6
=>2 =1+5-a+6
=>2 =12-a
=>-10=-a
=>10 =a
Answered by
12
AnswEr:-
Your answer is 10.
ExplanaTion:-
Given:-
- Cubic polynomial, is divided by (x-1) and leaves Remainder 2.
To Find:-
- The value of 'a' by using remainder theorem.
So Here,
It is given that when is divided by (x-1) then it leaves 2 as Remainder.
So If we subtract 2 from the given cubic polynomial then the resulted polynomial should be completely divisible by (x-1).
So lets subtract:-
x³+5x²-ax+4 is completely divisible by (x-1).
So we can say that is a factor of .
Thus by remainder theorem we get,
(x-1) is a factor of , so when we put the value of x in the above polynomial then it must be equal to 0.
So by putting the value of x we get,
The required value of a is 10.
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