If P-x-1-5x-1-5x-amp-Q-x-1-5x-1-5x- then P-x-Q-x- will be11-25x-2-1-25x-2-1-5x-2-1-5x-21-25x-2-1-25x-2

The correct option is C (1+5x)^2/(1 5x)^2Given, P(x) =1+5x/1 5x and Q(x) =1 5x/1+5x nbsp; ∴ P(x)/Q(x) = 1+5x/1 5x/1 5x/1+5x = (1+5x)(1+5x)/(1 5x)(1 5x) = ( ...

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Byju's Answer

Standard IX

Mathematics

Division Algorithm for Polynomial

If P(x)=1+5x/...

Question

If $P (x) = \frac{1 + 5 x}{1 - 5 x} & Q (x) = \frac{1 - 5 x}{1 + 5 x},$ then $\frac{P (x)}{Q (x)}$ will be

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\frac{1 - 25 x^{2}}{1 + 25 x^{2}}

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

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\frac{1 + 25 x^{2}}{1 - 25 x^{2}}

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Solution

The correct option is C $\frac{(1 + 5 x)^{2}}{(1 - 5 x)^{2}}$
Given, $P (x) = \frac{1 + 5 x}{1 - 5 x}$
$a n d Q (x) = \frac{1 - 5 x}{1 + 5 x}$

$∴ \frac{P (x)}{Q (x)} = \frac{\frac{1 + 5 x}{1 - 5 x}}{\frac{1 - 5 x}{1 + 5 x}} = \frac{(1 + 5 x) (1 + 5 x)}{(1 - 5 x) (1 - 5 x)} = \frac{(1 + 5 x)^{2}}{(1 - 5 x)^{2}}$

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Similar questions

Q. One of the factors of (25x² – 1) + (1 + 5x)² is
(a) 5 + x
(b) 5 – x
(c) 5x – 1
(d) 10x

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.

(i)

(ii)

(iii)

(iv)

(v)

Q. If

P (x) = \frac{1 + 5 x}{1 - 5 x} & Q (x) = \frac{1 - 5 x}{1 + 5 x},

then

\frac{P (x)}{Q (x)}

will be

Q. If

P (x) = \frac{1 + 5 x}{1 - 5 x} & Q (x) = \frac{1 - 5 x}{1 + 5 x},

then

\frac{P (x)}{Q (x)}

will be

Q. If

5 x + \frac{1}{5 x} = 23

and

5 x - \frac{1}{5 x} = 17

, find the value of

25 x^{2} - \frac{1}{25} x^{2}

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If P(x)=1+5x1−5x & Q(x)=1−5x1+5x, then P(x)Q(x) will be

The correct option is C (1+5x)2(1−5x)2Given, P(x)=1+5x1−5x and Q(x)=1−5x1+5x ∴ P(x)Q(x)=1+5x1−5x1−5x1+5x=(1+5x)(1+5x)(1−5x)(1−5x)=(1+5x)2(1−5x)2

If $P (x) = \frac{1 + 5 x}{1 - 5 x} & Q (x) = \frac{1 - 5 x}{1 + 5 x},$ then $\frac{P (x)}{Q (x)}$ will be