Question

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?

Answer 1

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 2

Hii

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