Question

Verify that 1 and 2 are the zeros of the polynomial p(x)=(x - 1)(x-2).

Answer 1

To Verify :

1 and 2 are the zeroes of given polynomial.

Solution:

(x-1) (x-2) =0

x(x-2) -1(x-2) =0

x²-2x-x+2=0

x²-3x+2=0........ (1)

Now, Substitute 1 in (1)

L. H. S=(1) ²-3(1) +2

=1-3+2

=-2+2=R.H.S

Therefore, 1 is the root of a given equation.

Now let substitute 2 in (1)

L. H. S=(2) ²-3(2) +2

=4-6+2

=-2+2

=0=R.H.S

Therefore, 2 is the root of a given polynomial.

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Answer 2

STEP BY STEP :-

let x = 1

(x -1) (x -2)

(1-1) (1-2)

0×(-1)

0

let x = 2

(x - 1) ( x - 2)

(2 - 1) (2 - 2)

1×0

0

Singh's 1 and 2 is prove as zero of the polynomial