If the third term in the binomial expansion of ( 1 + x ) m is - 1 8 x 2 , then the rational value of m is Options: A . &nbsp2 B . &nbsp12 C . &nbsp3 D . &nbsp4

Answer: Option B : B m c 2 = − 1 8 ⇒ m ( m − 1 ) 2 = − 1 8 ⇒ 4 m 2 − 4 m + 1 = 0 ⇒ ( 2 m − 1 ) 2 = 0 ⇒ m = 1 2

If the third term in the binomial expansion of (1+x)m is -18x2, then the rationa

Question

If the third term in the binomial expansion of

(1 + x)^{m}

is -

\frac{1}{8} x^{2}

, then the rational value of m is

Options:

A . 2

B . 12

C . 3

D . 4

Answer: Option B
:
B

m_{c_{2}} = - \frac{1}{8} \Rightarrow \frac{m (m - 1)}{2} = - \frac{1}{8} \Rightarrow 4 m^{2} - 4 m + 1 = 0 \Rightarrow (2 m - 1)^{2} = 0 \Rightarrow m = \frac{1}{2}

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