Given:

x³-6x²-x+30

To Find:

The value of alpha×beta+beta×gamma+gamma×alpha.

Solution:

The given polynomial is a polynomial of degree three.

Alpha (α), Beta (β), and Gamma (y) are the three roots of the polynomial.

Sum of roots

= Alpha (α)+Beta (β)+Gamma (y)

= -b/a                  

Sum of the product of two roots

= alpha×beta+beta×gamma+gamma×alpha.

= c/a

Product of roots

=Alpha (α)×Beta (β)×Gamma (y)

=-d/a

Where,

a is the coefficient of x³

b is the coefficient of x²

c is the coefficient of x

d is the constant

According to the question:

alpha×beta+beta×gamma+gamma×alpha.

= c/a

= -1/1

Hence,  the value of alpha×beta+beta×gamma+gamma×alpha is -1

Verified answer

Answer:αβ+β*gamma+gamma*α=-1

Step-by-step explanation:a=1,b=-6,c=-1,d=30

:αβ+β*gamma+gamma*α=c/a

=-1/1

=-1

therefore,alpha*beta+beta*gamma+gamma*alpha=-1

hope it helps you

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