Question

Srinivas saw a cuboid for his project but not interested to disclose the details of length,
breadth and height and gave the following polynomial x - 6x2 + 11x - 6. Find its
dimensions.​

Answer 1

Question-

Find the length, breadth and height of cuboid whose volume is

x³ - 6x² + 11x - 6​

Answer-

To find the length, breadth and height, we can factorise this volume to get the zeroes. The zeroes we get would be the length, breadth and height.

x³ - 6x² + 11x - 6​

= x³ - (5x² - x²) + (6x + 5x) - 6​

= x³ - 5x² + 6x - x² + 5x - 6

= x(x² - 5x + 6) - 1(x² - 5x + 6)

= (x - 1)(x² - 5x + 6)

= (x - 1)(x² - 2x - 3x + 6)

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

The zeroes are 1, 2 and 3.

Therefore,

Length = 1 unit

Breadth = 2 units

Height = 3 units