is a quartic, and is the remainder of the division
Which of the followings are true?
A.
B.
C.
This problem is a part of <Grade 10 CSAT Mock test> series .
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A.
f ( x ) = ( x − a ) ( x − b ) Q ( x ) + R ( x ) , and therefore, f ( a ) = R ( a ) .
∴ TRUE
B.
f ( a ) = R ( a ) , f ( b ) = R ( b ) .
The equation holds when f ( a ) = f ( b ) , which does not make any sense.
∴ FALSE
C.
Let R ( x ) = p x + q .
Note that R ( 0 ) = q , and we see that a f ( b ) − b f ( a ) = a R ( b ) − b R ( a ) = a b p + a q − a b p − b q = a q − b q = ( a − b ) q = ( a − b ) R ( 0 ) .
∴ TRUE
From the followings, only A and C are correct.