The value of x, for which the polynomials $x^{2} - 1$ and $x^{2} - 2 x + 1$ vanish simultaneously, is-

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Solution

The correct option is B $1$
$x^{2} - 1 = (x + 1) (x - 1) x^{2} - 2 x + 1 = x^{2} - x - x + 1 = x (x - 1) - 1 (x - 1) = {(x - 1)}^{2}$
Value of both polynomials become zero, when $x = 1$ .

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Similar questions

Question 1
Which one of the following is a polynomial?

A) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$
B) $\sqrt{2 x} - 1$
C) $x^{2} + \frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$
D) $\frac{x - 1}{x + 1}$

Q. Which of the following polynomials has (x + 1) as a factor?
I.

x^{3} + x^{2} + x + 1

II.

x^{4} + x^{3} + x^{2} + x + 1

III.

x^{4} + 3 x^{3} + 3 x^{- 2} + x + 1

II.

x^{3} + x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

Q. Determine which of the following polynomials has

(x + 1)

a factor:
(i)

x^{3} + x^{2} + x + 1

(ii)

x^{4} + x^{3} + x^{2} + x + 1

(iii)

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

(iv)

x^{3} - x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

Q. Simplify the following polynomials in the simplest form:

\frac{2 x + 5}{x + 1} + \frac{x^{2} + 1}{x^{2} - 1} - (\frac{3 x - 2}{x - 1})

Q. If

\frac{2 x}{x^{2} - 2 x + 1} = \frac{1}{2}

, then find the value of

{(x - \frac{1}{x})}^{2}

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The value of x, for which the polynomials x2−1 and x2−2x+1 vanish simultaneously, is-

The correct option is B 1x2−1=(x+1)(x−1)x2−2x+1=x2−x−x+1=x(x−1)−1(x−1)=(x−1)2Value of both polynomials become zero, when x=1.

The value of x, for which the polynomials $x^{2} - 1$ and $x^{2} - 2 x + 1$ vanish simultaneously, is-

The correct option is B $1$
$x^{2} - 1 = (x + 1) (x - 1) x^{2} - 2 x + 1 = x^{2} - x - x + 1 = x (x - 1) - 1 (x - 1) = {(x - 1)}^{2}$
Value of both polynomials become zero, when $x = 1$ .