Let $ N $ be the product of non-real roots of $ x^{4}-4 x^{3}+6 x^{2}-4 x=9999 $, then sum of digits of $ N $ equals

Question

Let $ N $ be the product of non-real roots of $ x^{4}-4 x^{3}+6 x^{2}-4 x=9999 $, then sum of digits of $ N $ equals,

MARKS App · Accepted Answer

x 4 − 9 x 3 + 6 x 2 − 4 x + 1 = 10000 ⇒ x − 1 4 = 100 2 ⇒ x − 1 2 = 100 or 100 i 2 where i = − 1 For non-real roots, x − 1 2 = 100 i 2 ⇒ x = + 10 i , 1 − 10 i So, N = 1 + 10 i 1 − 10 i = 1 + 100 = 101 Sum of digits of N = 1 + 0 + 1 = 2

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