Question

Let P be the product of the real roots of x4 − 4x3 + 6x2 − 4x = 2005. Find the greatest integer less than or equal to (−P).

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Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Concept:

A polynomial is an algebraic statement in which all of the variables' exponents must be whole numbers. In any polynomial, the exponents of the variables must be non-negative integers. A polynomial is made up of both constants and variables.

Given:

The polynomial x⁴-4x³+6x²-4x+1 = 2005.

The product of real roots is P.

Find:

The value of -P.

Solution:

$x^{4}-4 x^{3}+6 x^{2}-4 x+1=2006\\\\(x-1)^{4}=2006 \\\\(x-1)^{2}=\sqrt{2006} \\\\x=1+\sqrt[4]{2006}, 1-\sqrt[4]{2006} \\\\P=1-\sqrt{2006}\\\\-P=\sqrt{2006}-1 \\\\-P=44-1\\-P = 43$

Hence, the value of -P is 43.