1put x=3
1.p(5)=3p(1).p(-1)
put x=1, we get p(-1)=-3
p(5)= -9p(1)
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)?
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14 Answers
1can anyonr kindly post the solution , or atleast give a hint to solve it ?
341Ok 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)
1as 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
1hindi 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]