Question

verify whether the following are zeros of polynomial
$p(x) = {x}^{2} - 1 \: \: and \: x = - 1 \: and \: 1$
​

Answer 1

Answer :

Yes

Solution :

For any number to be the zero of the given polynomial , when substituted in place of the variable of the polynomial gives the result as 0 . If the result comes out to be other than 0 , the number is not a zero of polynomial .

1. When x = -1

P(x) = x² - 1

P(-1) = (-1)² -1

P(-1) = 1 - 1

P(-1) = 0

2. When x = 1

P(x) = x² - 1

P(1) = 1² -1

P(1) = 1-1

P(1) = 0

Yes , both -1 and 1 are the zeroes of x² -1 since remainder in each case comes out to be 0 .