Question

Find the positive value for m for which the coefficient of x2 in the expansion (1+x)m is 6

Answer 1

AnswEr:

We know that the coefficient of $\sf{x}^{r}$ in $\sf{(1+x)^n\:is}$ $\sf{^nC_r}$.

Therefore, coefficients of x² in $\sf{(1+x)^m}$ is $\sf{^mC_2}$

It is given that the coefficient of x² in $\sf{(1+x)^m}$ is 6 .

$\therefore \qquad \sf {}^{m} C_2 = 6 \\ \\ \implies \sf \: \frac{m(m - 1)}{2!} = 6 \\ \\ \implies \sf \: {m}^{2} - m = 12 \\ \\ \implies \sf \: {m}^{2} - m - 12 = 0 \\ \\ \implies \sf \: (m - 4)(m + 3) = 0 \\ \\ \implies \sf \: m - 4 = 0 \\ \\ \implies \sf \: m = 4 \qquad \sf \: \: ( \: m + 3 \neq \: 0 \: )$

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Binomial Expression :

An algebraic expression containing two terms in called a binomial Expression.