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?

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Answer 1

Answer:

24x² + 25x - 47ax - 2 = -8x - 3 - 53ax - 2

24x² + 25x - 47ax - 2 = -8x - 53ax - 5

24x² + 33x + 6ax + 3 = 0

8x² + 11x + 2ax + 1 = 0

x = 2a

8(2a)² + 11(2a) + 2a(2a) + 1 = 0

32a² + 22a + 4a² + 1 = 0

36a² + 22a + 1 = 0

D = 22² - 4(36)(1) = 340

a = (-22 + 2√85)/72 = (-11 + √85)/36

a = (-11 - √85)/36