Question

22. Verify whether 1 and -1 are zeroes of the polynomial x²-1 or not​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Polynomial is}\;\mathsf{x^2-1}$

$\underline{\textsf{To find:}}$

$\textsf{Verrify whether 1 and -1 are zeros of}$

$\textsf{the given polynomial or not}$

$\underline{\textsf{Solution:}}$

$\textsf{Let}\;\mathsf{P(x)=x^2-1}$

$\implies\mathsf{P(x)=x^2-1^2}$

$\textsf{Using the identity,}$

$\boxed{\mathsf{a^2-b^2=(a-b)(a+b)}}$

$\implies\mathsf{P(x)=(x-1)(x+1)}$

$\textsf{Now}$

$\textsf{P(x)=0}$

$\implies\mathsf{(x-1)(x+1)=0}$

$\implies\mathsf{x=1,-1}$

$\therefore\textsf{1 and -1 are zeros of P(x)}$

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Answer 2

$\sf { \underline{SOLUTION}}$

TO VERIFY

1 and -1 are zeroes of the polynomial x²-1 or not

CONCEPT TO BE IMPLEMENTED

If zeroes of a polynomial are given then the polynomial is

= x² - ( Sum of the zeroes ) x + ( Product of the Zeros)

EVALUATION

Here it is given two zeroes of a polynomial 1 and -1

Sum of the zeroes = 1 - 1 = 0

Product of the Zeroes = 1 × ( - 1 ) = - 1

Hence the required polynomial is

= x² - 0x - 1

= x² - 1

∴ 1 and -1 are zeroes of the polynomial x² - 1

Hence verified

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