What are the coordinates of the 2 points where y=2X-X^3/2 meets the x-axis?

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Answer 1 · 2017-12-13T17:49:09

#(0,0) & (4,0).#

The curve # C : y=2x-x^(3/2)# intersects the #X-# Axis, we

must have, #y=0.#

#:. 2x-x^(3/2)=0.#

#:. x(2-x^(1/2))=0.#

#:. x=0, or, x^(1/2)-2=0, i.e., x^(1/2)=2.#

# :. x=0, or, x=2^2=4.#

Hence the reqd. points of intrersection are, #(0,0) & (4,0).#