Question

14. Find a cubic polynomial with the sum sum of the product of its zeroes taken two at a time and product taken at a time and product of its zeroes are 3,-1/2,5/4 respectively​

Answer 1

Answer:

4x³ - 12x² - 2x - 5

Step-by-step explanation:

Given :

Let a, b, c be the zeroes of the cubic polynomial

Sum of the zeroes = a + b + c = 3

Sum of product of zeroes taken two at a time = ab + bc + ca = - 1/2

Product of zeroes = abc = 5/4

Cubic polynomial = k{ x³ - (a + b + c)x² + (ab + bc + ca)x - abc }

Where k ≠ 0

= k{ x³ - 3x² + (-1/2)x - 5/4 }

= k( x³ - 3x² - x/2 - 5/4 )

When k = 4

= 4( x³ - 3x² - x/2 - 5/4 )

= 4x³ - 12x² - 2x - 5

Therefore the cubic polynomial is 4x³ - 12x² - 2x - 5