enough ,now solve this:

Let P(x) be the non constant polynomial of smallest degree such that (x − 4)P(x2 − 4) = xP(x − 2)P(x − 4). What is P(5)?

14 Answers

1
thumbsdown007 ·

put x=3

1.p(5)=3p(1).p(-1)

put x=1, we get p(-1)=-3

p(5)= -9p(1)

6
AKHIL ·

and wat is P(1)??
:)

1708
man111 singh ·

P(5) = 45

341
Hari Shankar ·

put your money on man111 :D

1
learner ·

can anyonr kindly post the solution , or atleast give a hint to solve it ?

1
learner ·

@theprophet sir ,a hint ?

341
Hari Shankar ·

Ok try this.

First prove that the leading coefficient of P(x) is 1

Next prove that -4 and 0 are necessarily roots of the polynomial. So that degree of P(x)≥2

Find the quadratic satisfying the equation.

Now find P(5)

1
learner ·

thanks sir got it [1]

1
kunl ·

bade samjhdaar jaan padta ho bhaya[3][3]

1
learner ·

as sir told , once we prove the leading coefficient is 1 and and coeffiecent of x^0 is 0,our problem is done ..
we can prove them by assuming
P(x)=Σaixi
and putting it in the relation

after that put x=0 ...in the relation ,we will then get
P(-4)=0,telling us the other root

hence the degree has to be greater or equal to 2 , as we have alrdy got two roots..
so the minimum degree is 2 ..
hence
P(x)=x(x+4)...
P(5)=45

1
learner ·

@kunl i dont get hindi...is he something kind of offending me ???

1
kunl ·

hindi hai ham vatan hai hindustan hamara

dude tell me one thing when u don't get hindi how can u tell if i wrote in hindi OR french?.salu play madam musai[3]

1
samagra Kr ·

perfectly okay

6
AKHIL ·

:D
lol

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