Question

p,q,r are the Roots of x³-5x²+3 ,then |(p-2)(q-2)(r-2)| is

Answer 1

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• $\boxed{ |(p-2) (q-2) (r-2)| = 9}$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

Since $p, q, r$ are the roots of the given equation,

$\to x^3 - 5x^2 + 3$

$\:\:\:\:= (x-p) (x-q) (x-r)$

Substituting x = 2, we get

$\to 2^3 - 5.2^2 + 3$

$\:\:\:\:= (2-p) (2-q) (2-r)$

$\to 8 - 20 + 3$

$\:\:\:\:= -(p-2) (q-2) (r-2)$

$\to - 9 = -(p-2) (q-2) (r-2)$

$\to (p-2) (q-2) (r-2) = 9$

$\to |(p-2) (q-2) (r-2)| = 9$