Question

Check whether 1 is a zero of the polynomial p(x) =x^6-x^5-x^4-x^3-x^2-x+1=0

Answer 1

Answer:

Step-by-step explanation:

Answer: Zeros of (I) are a=0, 3u/4; zero of (II) is r= 4/3π

Solution:

The Zeros of the polynomials

3au - 4a² ………………………………….(I) and

3πr - 4 ……………………………………..(II)

can be found by solving the two equations

3au - 4a² = 0 …………………………………………………………………….…………(1)

and 3πr - 4 = 0 ……………………………………………………………………….…..(2)

Since (I) is a polynomial of degree two in a, it will have two roots; and (II) being a first degree polynomial in r will have only one root. (1) being a quadratic in a can be solved by factorisation or by using the formula or by method of completion of square.

Factorizing (1),

a(3u - 4a) = 0

Or, a = 0 , 3u - 4a = 0

Or, a = 0, 3u = 4a

Or, a=0, a = 3u/4

∴ The zeros of the polynomial 3au - 4a² are

a = 0 and a = 3u/4

The zero of (2) is obtained by solving for r.

3πr - 4 = 0

Or, 3πr = 4 (Taking -4 to right-side and changing the sign)

Or, r = 4/3π

∴The zero of the polynomial 3πr - 4 is

r = 4/3π

85 views · View 1 Upvoter · Answer requested by Abha Dewangan