If roots of an equation xn−1=0 are 1,a1,a2,…,an−1,, then the value of (1–a1 )(1–a2 )......(1–an–1) will be

xn−1x−1=x−a1x−a2…x−an−1xn−1=(x−1)x−a1x−a2x−a3….x−an−1nxn−1=1x−a1x−a2x−a3…..x−an−1+(x−1)(1)x−a2x−a3…x−an−1···+(x−1)x−a1x−a2x−a3 Sub x=1⇒n=1−a11−a2···1−an−1

If roots of an equation xn−1=0 are 1,a1,a2,…,an−1,, then the value of (1–a1 )(1–a2 )......(1–an–1) will be

xn−1x−1=x−a1x−a2…x−an−1xn−1=(x−1)x−a1x−a2x−a3….x−an−1nxn−1=1x−a1x−a2x−a3…..x−an−1+(x−1)(1)x−a2x−a3…x−an−1···+(x−1)x−a1x−a2x−a3 Sub x=1⇒n=1−a11−a2···1−an−1

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If roots of an equation $x^{n} - 1 = 0 are 1, a_{1}, a_{2}, \dots, a_{n - 1},$ , then the value of (1–a₁ )(1–a₂ )......(1–a_n–1) will be

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

n²

nⁿ

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} \frac{x^{n} - 1}{x - 1} = (x - a_{1}) (x - a_{2}) \dots (x - a_{n - 1}) \\ x^{n} - 1 = (x - 1) (x - a_{1}) (x - a_{2}) (x - a_{3}) \dots . (x - a_{n - 1}) \\ n x^{n - 1} = 1 (x - a_{1}) (x - a_{2}) (x - a_{3}) \dots . . (x - a_{n - 1}) + (x - 1) (1) (x - a_{2}) (x - a_{3}) \dots (x - a_{n - 1}) \cdot \cdot \cdot + (x - 1) (x - a_{1}) (x - a_{2}) (x - a_{3}) \\ Sub x = 1 \\ \Rightarrow n = (1 - a_{1}) (1 - a_{2}) \cdot \cdot \cdot (1 - a_{n - 1}) \end{array}$