Question

two zeroes of polynomial x^3-6^2+11x-6 are 2 and 3 the third zero​

Answer 1

Answer:

Given,

2 and 3 are the zeroes of polynomial x³-6x²+11x-6

the factors of p(x) = x³-6x²+11x-6 will be (x-2) , (x-3)

Given polynomial is a cubic polynomial

x³ - 6x² + 11x - 6 = (x -2)(x - 3)(ax + b)

x³ - 6x² + 11x - 6 = (x² - 5x - 6)(ax + b)

x³ - 6x² + 11x - 6 = ax³ - 5ax² + 6ax + bx² - 5bx + 6b

x³ - 6x² + 11x - 6 = ax³ - x²(5a - b) + x(6a - 5b) + 6b

by comparing coefficients of x on both sides,

a = 1 and b = - 1

Thus, the factor (ax + b) = (x - 1) Or x = 1

The third zero is : x = 1