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If $m$ and $n$ are the zeroes of the polynomial $3x^2+11x−4$, find the values of $\frac{m}{n}+\frac{n}{m}$
Given: $m$ and $n$ are the zeroes of the polynomial $3x^2+11x−4$.
To do: To find the values of $\frac{m}{n}+\frac{n}{m}$.
Solution:
As given, zeroes of the polynomial $3x^2+11x -4$ are $m$ and $n$
$\Rightarrow 3(m)^2 + 11(m) -4 = 0$
$\Rightarrow 3m^2+ 11m -4 = 0$
$\Rightarrow 3m^2 +12m -m - 4 = 0$
$\Rightarrow3m( m+ 4) - 1( m + 4) =0$
$\Rightarrow (3m - 1) ( m+4) = 0$
$\Rightarrow (3m - 1) = 0$ (or) $(m +4 ) = 0$
$\Rightarrow m = \frac{1}{3}$ or m = -4$
If we replace n in x place , we get the same values
Hence , $\frac{m}{n} + \frac{n}{m} = 1 + 1 =2$
 
Updated on: 10-Oct-2022
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