# Solve this equation: `tan^2 x - 3tan x + 2 = 0`

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Solve `tan^2x-3tanx+2=0`

Note that this is quadratic in tan(x).

Thus we can factor as (tanx-2)(tanx-1)=0

By the zero product property we have

(1) tanx=1 ==> `x=pi/4 +kpi` for integer k

(2) tanx=2 ==> `x=tan^(-1)2~~1.107+kpi`

The graph:

`tan^2x-3tanx+2=0`

Let

`tanx=y`

So ,equation reduces to

`y^2-3y+2=0`

`y^2-2y -y+2=0`

`y(y-2)-1(y-2)=0`

`(y-2)(y-1)=0`

`` either y=2 or y=1

if `tan(x)=2`

`=tan((7pi)/20)`

`x=npi+(7pi)/20` ,where n is an integer.

if `tan(x)=1`

`=tan(pi/4)`

`x=n_1pi+pi/4` ,where `n_1` is an integer.