Question

pleaseeeeeeeeeeeeeeeeeee answer this question quickly it's urgent.
If p(x) = x^3 - 3x^2 + 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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Answer 1

Answer:

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