Question

Find the cubic polynomial which sum of its zeroes , sum of its product of its zeroes take two at time and product of its zeroes as 2, -7 and -14 respectively

Answer 1

Answer:

$\large{\underline{\boxed{\sf x^3 - 2x^2 - 7x - 14}}}$

Step-by-step explanation:

Let the zeroes of the cubic polynomial be α, β and γ respectively.

According to the question ;

Sum of zeroes = 2

⇒ α + β + γ = 2

Sum of the product of the roots taken two at a time = - 7

⇒ αβ + βγ + γα = - 7

Product of zeroes = - 14

⇒ αβγ = - 14

Now, we know that -

The cubic polynomial is given by -

⇒ x³ - (α + β+γ)x² + (αβ + βγ+αγ)x - αβγ

⇒ x³ - 2x² - 7x - 14

Hence, the required cubic polynomial is (x³ - 2x² - 7x - 14).

Answer 2

Solution :-

Let α , β and y be be the zeroes of the cubic polynomial.

Given :-

• Sum of zeroes = 2

» α+β+y = 2

• Sum of product of zeroes = -7

» αβ + βy + αy = -7

• Product of zeroes = -14

» αβy = -14

_______________________________

We know that :-

» x³ -( α+β+y)x² +(αβ+βy+αy)x -αβy

_____________________[Put value]

» x³ - (2)x² + (-7)x - (-14)

» x³ - 2x² - 7x+ 14

_______________[Answer]

So, the cubic polynomial is x³ - 2x² - 7x +14

_______________________________