Tangent at P(2,8) on the curve `y=x^(3)` meets the curve again at Q. Find coordinates of Q.
Tangent at P(2,8) on the curve `y=x^(3)` meets the curve again at Q.
Find coordinates of Q.
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It is concept of tangent that if two intersection point coincides then that line is tangent to that point.
Therefore, we considered x = 2 will be a repeated root of equation. Although we can find this result algebraically that x = 2 is repeated root of equation
x^3 - 12x + 16 = 0
⇒ (x - 2) (x^2 + 2x - 8) = 0
⇒ (x - 2) (x - 2) (x + 4) = 0
⇒ x = 2, 2, -4
Hence, x = -2 is repeated root and other root is x = -4.
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