Question

if one zero of the polynomial p(x)=x3-6x2+11x-6 is 3, find the other two zeros.​

Answer 1

Step-by-step explanation:

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Answer 2

The other two zeroes of the polynomial are 1 and 2.

Step-by-step explanation:

We are given the following polynomial:

$p(x)=x^3-6x^2+11x-6$

One of the roots of given polynomial is 3.

$p(3)=(3)^3-6(3)^2+11(3)-6 = 0$

We have to find the other two roots.

The polynomial can be factorized as

$p(x)=x^3-6x^2+11x-6\\\\g(x) = \dfrac{x^3-6x^2+11x-6}{x-3}\\\\g(x) = x^2-3x +2\\g(x) = 0\\\Rightarrow x^2-3x +2= 0\\\Rightarrow x^2 - x -2x + 2 =0\\\Rightarrow x(x-1)-2(x-1)=0\\\Rightarrow (x-1)(x-2) = 0\\\Rightarrow x = 1, x = 2$

Thus, other two zeroes of the polynomial are 1 and 2.

#LearnMore

Two zeroes of p(x)= x3-6x2+11x-6 are 2 and 3. Find the third zero ?

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