When two lines meet!! 3

Algebra Level 5

Find the number of roots of equation $f(x) =|\log_{10}(nx + 100002)| - (n^2 x^2 + 4nx + 9)$ .

$n$ is equal to 1.

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Aryan Sanghi
May 12, 2020

$f(x) =|log(nx + 10^5 + 2)| - (n^2 x^2 + 4nx + 9) = 0$

$|log(nx + 10^5 + 2)| = (n^2 x^2 + 4nx + 9)$

So, we have to basically find points of intersection of $y =|log(nx + 10^5 + 2)|$ and $y = (n^2 x^2 + 4nx + 9)$

Here is the graph

So, we can see that they intersect at three points. So, there are 3 roots

How do you make sure that the curves will intersect in the region $[-100002,-100001]$ ?

A Former Brilliant Member - 1 year, 1 month ago

By intermediate value theorem sir. And sir, logically also, they'll intersect, isn't it?

Aryan Sanghi - 1 year, 1 month ago