Statement - 1: The tangent at x = 1 , to the curve y = x 3 − x 2 − x + 2 again meets the curve at x = 0 Statement - 2: For third degree equation when the equation of a tangent solved, with the given c

Question

Statement - 1: The tangent at x = 1 , to the curve y = x 3 − x 2 − x + 2 again meets the curve at x = 0 Statement - 2: For third degree equation when the equation of a tangent solved, with the given curve repeated roots are obtained at point of tangency.

TestHub · Accepted Answer

When x = 1 , y = 1 . d x d y ​ = 3 x 2 − 2 x − 1 ⇒ ( d x d y ​ ) x = 1 ​ = 0 ⇒ equation of the tangent is y = 1 Solving with the curve, x 3 − x 2 − x + 2 = 1 ⇒ x 3 − x 2 − x + 1 = 0 ⇒ ( x − 1 ) 2 ( x + 1 ) = 0 ⇒ x = − 1 , 1 (1 is repeated root) ∴ The tangent meets the curve again at x = − 1 , not at x = 0 . So Statement-1 is false and Statement-2 is true.

Mathematics - Application of Derivative Question with Solution | TestHub

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