The equation 24x2+25x−47ax−2=−8x−3−53ax−2 is true for all values of x≠2a, where a is a constant.
What is the value of a?
A) -16
B) -3
C) 3
D) 16
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Answers
Answer:
Kingrk
Kingrk Ace
24x2+ 25x − 47 divided by ax − 2 is equal to
−8x −3 with remainder −53,
it is true that (−8x − 3)(ax − 2) − 53 = 24x2 +25x −47.
(This can be seen by multiplying each side of the given equation by ax − 2).
This can be rewritten as −8ax2+ 16x − 3ax = 24x2+ 25x − 47.
Since
the coefficients of the x2
-term have to be equal on both sides of the equation,
−8a = 24, or a = −3.
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Answer:
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Rolling everything over to the left hand side we get
Rolling everything over to the left hand side we get24x2+33x+3+6ax=0
Rolling everything over to the left hand side we get24x2+33x+3+6ax=0 and if this has to be true for all x≠2a, 6ax has to cancel out everything left of it, in other words a cannot be a constant. It must be equal to
Rolling everything over to the left hand side we get24x2+33x+3+6ax=0 and if this has to be true for all x≠2a, 6ax has to cancel out everything left of it, in other words a cannot be a constant. It must be equal toa=−(4x+112+12x), x≠0.
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