Latest TCS Aptitude Question SOLUTION: If p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3 and 4, and p(0)=48, what is p(5) a)48 b)24 c)0 d)50

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If p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3 and 4, and p(0)=48, what is p(5)
a)48
b)24
c)0
d)50

Asked In TCS krishnaprasad TATA (11 years ago)

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Garima  (11 years ago)

48

if 1 is a root then x-1 is a factor of p(x)
similarly x-2 is a factor,x-3 ,x-4 are factors

but p(x) is 4th degree polynomial therefore it can be in the form

p(x) = k(x-1)(x-2)(x-3)(x-4) , where k is a constant

but given p(0) =48

therefore 24 k =48

k=2

p(x) =2(x-1)(x-2)(x-3)(x-4)

p(5)= 2*4*3*2*1 = 48

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