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In how many points the graph of f(x)=x^3...

In how many points the graph of `f(x)=x^3+2x^2+3x+4` meets the `x axis` ?

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The correct Answer is:
One
`f(x) = x^(3) + 2x^(2) + 3x + 4`
`rArr f'(x) = 3x^(2) + 4x + 3`
Now `f'(x) = 3x^(2) + 4x + 3 = 0` has nonereal roots.
Hence, graphs has no turning point.
Also when `x to infty, f(x) to infty` and when `x to infty, f(x) to infty`
Hence, graph of `y = f(x) meets the x-axis only once.
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