Question

If a and b are the roots of equation $x^2$ + 4x + p = 0 where P= ${\sum }_{r=0}^n$ $n_{c_r}$ $\frac{1+rx}{(1+nx{)}^r}$$(-1{)}^r$
then the value of $|a-b|$ is

• A. 2
• B. 6
• C. 4
• D. None of these

Answer 1

The correct option is C

4

$p={\sum }_{r=0}^n{n}_{cr}{\left(\frac{-1}{1+nx}\right)}^r+{\sum }_{r=0}^n{n}_{cr}\frac{(-1{)}^{r}rx}{(1+nx{)}^r}={(1-\frac{1}{1+nx})}^n+x{\sum }_{r=1}^n{}^{n-1}{C}_{r-1}\frac{(-1{)}^{r}r}{(1+nx{)}^r}={\left(\frac{nx}{1+nx}\right)}^n-\left(\frac{nx}{1+nx}\right){(1-\frac{1}{1+nx})}^{n-1}=0\therefore |a-b|=4$