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Byju's Answer

Standard IX

Mathematics

Visualisation of Addition of Polynomials

Find all poly...

Question

Find all polynomials P(x) with real coefficients such that (x-8)P(2x)=8(x-1)P(x) .

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Similar questions

Q. Let

P (x)

be a polynomial with real coefficients such that

P ({sin}^{2} x) = P ({cos}^{2} x)

, for all

x ϵ [0, π / 2]

. Consider the following statements:
I.

P (x)

is an even function.
II.

P (x)

can be expressed as a polynomial in

(2 x - 1)^{2}

.
III.

P (x)

is a polynomial of even degree.
Then

Q. If

P (x)

be a polynomial with real coefficients such that

P ({sin}^{2} x) = P ({cos}^{2} x)

, for all

x \in [0, \frac{π}{2}]

. Consider following statements:

I.

P (x)

is an even function.
II.

P (x)

can be expreesed as a polynomial in

(2 x - 1)^{2}

III.

P (x)

is a polynomial of even degree.

Q. Determine all polynomial

P (x)

with rational coefficient so that for all

x

with

| x | \leq 1

;

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

Q. Let

P

be a non-zero polynomial such that

P (1 + x) = P (1 - x)

for all real

x

, and

P (1) = 0

. Let

m

be the largest integer such that

(x - 1)^{m}

divides

P (x)

for all such

P (x)

. Then

m

equals

Q. Let

P (x) = x^{2} + b x + c

be a quadratic polynomial with real coefficients such that

1 \int 0 P (x) d x = 1

and

P (x)

leaves remainder

5

when it is divided by

(x - 2) .

Then the value of

9 (b + c)

is equal to :

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