Question

verify whether the indicated numbers are zeroes of the polynomials corresponding to them in the following cases : p(x)=x³-6x²+11x-6;x=1,2,3​

Answer 1

Step-by-step explanation:

We are given the following polynomial:

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

3

−6(3)

2

+11(3)−6=0

We have to find the other two roots.

The polynomial can be factorized as

\begin{gathered}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\end{gathered}

p(x)=x

3

−6x

2

+11x−6

g(x)=

x−3

x

3

−6x

2

+11x−6

g(x)=x

2

−3x+2

g(x)=0

⇒x

2

−3x+2=0

⇒x

2

−x−2x+2=0

⇒x(x−1)−2(x−1)=0

⇒(x−1)(x−2)=0

⇒x=1,x=2

Hope it was correct and helpful to u