Oxford University MAT 2019 Solved Papers

Question : 1 of 10

Marks: +1, -0

The equation

x^3-300 x=3000

has

no real solutions.
exactly one real solution.
exactly two real solutions.
exactly three real solutions.
infinitely many real solutions.

Validate

Solution:

A The cubic on the left-hand side,

x^3-300 x

, has turning points at

x=± 10

, and at

x=-10

the cubic has value 2000 . Since the right-hand side of the equation is greater than 2000 , there can only be one root to the equation.
The answer is (b)

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