If p(x)=x3−3x2+2x+5 and p(a)=p(b)=...
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If ( p(x)=x^{3}-3 x^{2}+2 x+5 ) and ( p(a)=p(b)=p(c)=0, ) then the value of ( (2-a)(2-b)(2-c) ) is
(A) 3
(B) 5
(C) 7
(D) 9

JEE/Engineering Exams
Maths
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 If p(x)=x3−3x2+2x+5 and p(a)=p(b)=p(c)=0, then the value of (2−a)(2−b)(2−c) is
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[
begin{array}{c}
p(x)=x^{3}-3 x^{2}+2 x+5
p(a)=p(b)=p(c)=0
end{array}
]
( Rightarrow quad x=a, b, c ) are
rosts of polynomial ( p(x) )
[
begin{array}{l}
Rightarrow p(x)=(x-a)(x-b)(x-c)
text { wher, } quad a+b+c=3
quad a b+b c+a c=2
quad a b c=-5
begin{aligned}
b(2)=&(2-a)(2-b)(2-c)
=& 2^{3}-3(2)^{2}+4+5
&=8-12+4+5
&=5
end{aligned}
end{array}
]
Option B.

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