if x is equals to x raised to the power 4 minus 2 x raise to power 3 minus 3 x raise to power 2 - 9 x + b is a polynomial such that when it is divided by x minus 1 and x + 1 leaving the remainder 5 and 19 respectively determine the remainders when f x is divided by x minus 2
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Answered by
3
Answer:
Step-by-step explanation:
x = 50
parush34:
no
Answered by
7
Answer:
Step-by-step explanation:
There is theorem known as “Polynomial Remainder Theorem” or “ Bezout’s Theorem”. It is Stated as -
A Polynomial f(x) if divided by a linear polynomial (x-a) leaves remainder which equals f(a).
So , getting back to our question -
f(x)=x4−2x3+3x2−ax+b
So , when it is divided by(x−1) it’ll leave a remainder = f(1) = 5 (Given).
f(1)=14−2×13+3×12−a×1+b=5
=>1−2+3−a+b=5
=>a−b=(−3)….Eqn(1)
Now , Similarly -
f(−1)=(−1)4−2×(−1)3+3×(−1)2−a×(−1)+b=19
=>1+2+3+a+b=19
=>a+b=13….Eqn(2)
Now , adding equations (1) and (2) , We’ll get -
(a+b)+(a−b)=(−3)+13
=>2a=10=>a=5
So , (a+b)=13 implies b=8
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