An expression was factorised as (x – 1)(x – 3)(x – 5)…(x – 99). What is the coefficient of x⁴⁹ in the expression?

Question

KnowledgeBoat · Accepted Answer

Given, Polynomial = (x - 1)(x - 3)(x - 5) ........ (x - 99) Here roots are 1, 3, 5, ....., 99. Let number of roots be n. The above sequence is in an A.P. with first term (a) = 1, common difference (d) = 2 and last term (an) = 99 By formula, ⇒ an = a + (n - 1)d ⇒ 99 = 1 + 2(n - 1) ⇒ 99 - 1 = 2(n - 1) ⇒ 98 = 2(n - 1) ⇒ n - 1 = ⇒ n - 1 = 49 ⇒ n = 50. Sum of roots = = 2500. For a polynomial of the form, (a - a1)(x - a2).......... The coefficient of xn - 1 is the negative of the sum of all roots. Thus, the coefficient of x49 = -2500. Hence, coefficient of x49 = -2500.

Mathematics

An expression was factorized as (x - 1)(x - 3)(x - 5) ….. (x - 99). What is the coefficient of x⁴⁹ in the expression ?

Factorisation

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Mathematics

An expression was factorized as (x - 1)(x - 3)(x - 5) ….. (x - 99). What is the coefficient of x49 in the expression ?

Factorisation

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An expression was factorized as (x - 1)(x - 3)(x - 5) ….. (x - 99). What is the coefficient of x⁴⁹ in the expression ?

An expression is factorized as (2x³ + 2x² + x)(x² - 2x + 2). Which of the following terms will appear in the simplest form of the above expression?
-2x³
3x³
6x³
x³