Question

2. Find a cubic polynomial with the sum, sum of the product of its zeroes
taken two at a time, and the product of its zeroes are 3, 0,- 4, respectively.​

Answer 1

Answer :

x³ + 3x² + 4

Step-by-step explanation :

Given,

sum of the zeroes = 3

sum of the product of its zeroes  taken two at a time = 0

the product of its zeroes = - 4

The cubic polynomial will be in the form of :

⇒ x³ - (sum of zeroes)x² + (sum of the product of its zeroes taken two at a time)x - (product of zeroes)

⇒ x³ - 3x² + (0)x - (-4)

⇒ x³ - 3x² + 0 + 4

⇒ x³ - 3x² + 4

Answer 2

$\huge\fbox \red{Solution:}$

Generally,

A cubic polynomial say, f(x) is of the form ax3 + bx2 + cx + d.

And, can be shown w.r.t its relationship between roots as.

⇒ f(x) = k [x3 – (sum of roots)x2 + (sum of products of roots taken two at a time)x – (product of roots)]

Where, k is any non-zero real number.

Here,

f(x) = k [x3 – (3)x2 + (-1)x – (-3)]

∴ f(x) = k [x3 – 3x2- x + 3)]

where, k is any non-zero real number.