Question

Lakshmi does not want to disclose the length breadth the height of a Cuboid of her project. she constructed a polynomial x3-6x2+11x-6 by taking the values of length, breadth and height as it 2 cries can you open the secret​

Answer 1

Answer:

Length , Breadth & Height = 1 , 2 , 3

Step-by-step explanation:

Length , Breadth & Height of a cuboid is given by

x³ - 6x² + 11x - 6

so we need to find the three roots of given equation to find

Length , Breadth & Height

x³ - 6x² + 11x  - 6 = 0

just by seeing we can see that x = 1 satisfies this

=> x - 1 is a factor of this

x³ - x² - 5x² + 5x + 6x - 6 = 0

=> x²(x - 1) - 5x(x - 1) + 6(x - 1) =0

=> (x-1)(x² - 5x + 6) = 0

=> (x -1)(x² - 2x - 3x + 6) = 0

=> (x -1)(x-2)(x-3) = 0

=> roots are 1 , 2, 3

Hence Length , Breadth & Height = 1 , 2 , 3

Answer 2

The length breadth the height of a Cuboid of her project is (x -1), (x-2), (x-3).

Step-by-step explanation:

Consider the information,

The provided polynomial $x^3-6x^2+11x-6$

The polynomial represents the volume of the cuboid.

$V=lbh$

Factor the polynomial as shown below:

Substitute x = 1 in above polynomial.

$1^3-6+11-6=0$

x-1 is a factor of the polynomial so divide the provided polynomial by x-1.

$\frac{x^3-6x^2+11x-6}{x-1}=x^2-5x+6$

Now factor out $x^2-5x+6$

$x^2-5x+6=x^2-2x-3x+6\\=x\left(x-2\right)-3\left(x-2\right)\\=(x-3)(x-2)$

Hence, the length breadth the height of a Cuboid of her project is (x -1), (x-2), (x-3).

#Learn more

If x=1 is one root of the equation x^3-6x^2+11x-6=0 find the other roots

https://brainly.in/question/6028414