Question

1 point

 If α,β,γ be the zeroes of the polynomial p(x) such that (α+β+γ)=3, (αβ+βγ+γα)=-10 and αβγ=-24 then p(x)=

​

Answer 1

Answer:

Step-by-step explanation:

ANSWER:-

We know the formula that

$x^3+(\alpha+\beta+\gamma)x^2-(\alpha\beta+\beta\gamma+\gamma\alpha)x+(\alpha\beta\gamma)$

We are given that:-

(α+β+γ)=3

(αβ+βγ+γα)= -10

αβγ= -24

Placing Values directly in the equation:

The Quadratic Equation formed is :-

$x^3+3x^2-(-10)x+(-24)$

$p(x)= x^3+3x^2+10x-24$ is the required Quadratic Equation.

Things to Remember:

$\alpha+\beta+\gamma = \frac{-b}{a}$

$\alpha\beta+\beta\gamma+\gamma\alpha = \frac{c}{a}$

$\alpha\beta\gamma = \frac{-d}{a}$