Question

If p is a real number and if the middle term in the expansion of ${(\frac{p}{2}+2)}^8$ is 1120, find p.

Answer 1

In the binomial expansion of ${(\frac{p}{2}+2)}^8$, we observe that $(\frac{8}{2}+1)th$ i.e., 5th term is the middle term

It is given that the middle term is 1120.

$\therefore T_5=1120$

${\Rightarrow }^8{C}_4{\left(\frac{p}{2}\right)}^{8-4}(2{)}^4=1120$

$\Rightarrow p^4=16$

$\Rightarrow p=\pm 2$

Hence, the real values of p is $\pm 2.$