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Q.

Consider the cubic function f(x) = x(x  2) (x  6). 

Which of the following is/are true? 

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a

Tangent curve drawn to the curve  y = f(x) at the point 4,-16, meets the curve again at the point (2, 0)

b

Tangent line drawn to the curve  y = f(x) at the point (3, -9), meets the curve again at the point 2,0

c

Tangent line drawn to the curve  y = f(x) at the point4,-16 , meets the curve again at the point (0, 0)

d

Tangent line drawn to the curve  y = f(x) at the point (1, 5), meets the curve again at the point 6,0

answer is A, B, C.

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Detailed Solution

For the function f(x) = (x – a) (x – b) (x – c) has three distinct zeroes. A tangent line drawn at the average of the two zeroes a and b, intersects the graph of ‘f’ again at the third zero. 

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