Sarthaks Test
0 votes
66 views
in Mathematics by (15.0k points)

Verify whether the following are zeroes of the polynomial, indicated against them.

(i) p(x) = x2 − 1, x = 1, − 1

(ii) p(x) = (x + 1) (x − 2), x = − 1, 2

(iii) p(x) = x2 , x = 0

1 Answer

0 votes
by (24.8k points)
selected by
 
Best answer

(i) If x = 1 and x = −1 are zeroes of polynomial p(x) = x2 − 1, then p(1) and p(−1) should be 0.

Here, p(1) = (1)2 − 1 = 0, and

p(− 1) = (− 1)2 − 1 = 0

(ii) If x = −1 and x = 2 are zeroes of polynomial p(x) = (x +1) (x − 2), then p(−1) and p(2)should be 0.

Here, p(−1) = (− 1 + 1) (− 1 − 2) = 0 (−3) = 0, and

p(2) = (2 + 1) (2 − 2 ) = 3 (0) = 0

(iii) If x = 0 is a zero of polynomial p(x) = x2, then p(0) should be zero. Here, p(0) = (0)2 = 0

Hence, x = 0 is a zero of the given polynomial.

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...