Question

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time and product of its zeroes are 2, -9, 8 respectively.​

Answer 1

Answer:

x³ - 2x² - 9x - 8 = 0

Step-by-step explanation:

Let x, y and z be the roots of the quadratic equation.

From the problem statement it is given that:

x + y + z = 2    ...(i)

xy + xz + yz = -9    ...(ii)

xyz = 8      (iii)

Equation (ii) can be written as:

⇒ x(y + z) + yz = -9

Substituting value of (y + z) from equation (i) and value of yz from equation (iii) into equation (ii)

⇒ x(2 - x) + 8/x = -9

=> 2x - x² + 8/x = -9

=> 2x² - x³ + 8 = -9x

=> x³ - 2x² - 9x - 8 = 0