Question

Il P(x) = x3 - 3x2 +2x +5 and
p(a)=P (b) = P(c) = 0
then find the value of
(2-a) (2-b) (2-c)​

Answer 1

Answer:

5

Step-by-step explanation:

Given, p(x) = x3 – 3x2 + 2x + 5

It is given that, p(a) = p(b) = p(c) = 0, which implies that a, b, c are the zeroes of the given cubic polynomial p(x).

∴sum of zeroes,

Sum of the product of zeroes taken two at a time

Product of zeroes =

Now, (2 – a) (2 – b) (2 – c) = [ 4 – 2b – 2a + ab ] [ 2 – c ]

= 8 – 4b – 4a + 2ab – 4c + 2bc + 2ac – abc

= 8 – 4(a + b + c) + 2(ab + bc + ac) – abc

= 8 – 4(3) + 2(2) – (–5) [ using (1), (2) and (3) ]

= 8 – 12 + 4 + 5 = 5//

Answer 2

Step-by-step explanation:

Hope you understand step by step solution of this question

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