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Question: If *x*<sub>1</sub>, *x*<sub>2</sub>, *x*<sub>3</sub>,…….*x*<sub>n</sub> are the roots of *x*<sup>n</...

If x1, x2, x3,…….xn are the roots of xn + ax + b = 0, then the value of (x1 – x2) (x1 – x3) (x1 – x4)……… (x1 – xn) is equal to

A

nx1 + b

B

n (x1)n–1

C

n(x1)n–1 + a

D

n(x1)n–1 + b

Answer

n(x1)n–1 + a

Explanation

Solution

xn + ax + b = (x – x1) (x – x2)….(x – xn)

⇒ (x – x2) (x – x3)….(x – xn) = xn+ax+b(x−x1)\frac{x^{n} + ax + b}{(x - x_{1})}

⇒ (x1 – x2) (x1 – x3)….(x1 – xn)

= lim⁡x→x1\lim _ { x \rightarrow x _ { 1 } } xn+ax+bx−x1\frac{x^{n} + ax + b}{x - x_{1}}

= nx1n–1nx_{1}^{n–1}+ a.

Hence (3) is correct answer.