The number of points of intersection of $f (x) = x^{3} - 9 x^{2} + 27 x - 27$ and $g (x) = x$ is

1.0

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1.00

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Solution

Given: $f (x) = x^{3} - 9 x^{2} + 27 x - 27$
$f (x)$ can be written as:
$f (x) = x^{3} + 3 (- 3) x^{2} + 3 (- 3)^{2} x - 3^{3} \Rightarrow f (x) = (x - 3)^{3}$
Whose graph, we can draw as:
Now, to find the number of points of intersection of $f (x) & g (x),$ let's draw both of them on the same graph as:
Thus, the graphs intersect each other at $1$ point.

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Similar questions

Find the maximum and minimum values, if any, of the following functions given by

(i) f(x) = (2x − 1)² + 3 (ii) f(x) = 9x² + 12x + 2

(iii) f(x) = −(x − 1)² + 10 (iv) g(x) = x³ + 1

Show that g(x) is a factor of f(x), where

f(x) = 2x³ − 9x² + x + 12, g(x) = 3 − 2x

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x).

f(x) = $2 x^{3} - 9 x^{2}$ + x + 12, g(x) = 3 - 2x

27 - x^{3} - 9 x^{2} + 27 x

(x^{3} + 9 x^{2} + 27 x + 27)^{25}

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