Question

Find the values of alpha + beta + gamma if f(x)= x^3-7x^2 + 6x + 8

Answer 1

Answer:

7

Step-by-step explanation:

There is a property which we need to remember that :

SUM OF ZEROES : Alpha + Beta + Gamma = -b / a

Now, what are alpha, beta and gamma?

Actually, they are the zeroes of a polynomial. So, here, the polynomial given is f(x) = x^3-7x^2 + 6x + 8.

Here, a = 1, b = -7, c = 6 and d = 8.

But, we do not need the value of 'd' or 'c' here. Only, 'a' and 'b' are needed in this case.

So, placing the values,

Alpha + Beta + Gamma = -b / a -----------> -(-7) / 1 = 7

HENCE, VALUE OF Alpha + Beta + Gamma = 7

MORE PROPERTIES TO KNOW :-

• THERE ARE THREE PROPERTIES THAT WE NEED TO REMEMBER FOR CUBIC POLYNOMIAL :

1. Alpha + Beta + Gamma = - b / a
2. Alpha * Beta * Gamma = - d / a

   3.(Alpha * Beta) + (Beta * Gamma) + (Gamma * Alpha) = c / a

• THERE ARE TWO PROPERTIES THAT WE NEED TO REMEMBER FOR QUADRATIC POLYNOMIAL :

1. Alpha + Beta = - b / a
2. Alpha * Beta = c / a

Answer 2

ANSWER = 7

f(x) = x³ - 7x² + 6x + 8

Here:-

a = 1 , b = - 7 , c = 6, d = 8

We know that:-

α + β + γ = - b/a

α + β + γ = -(-7)/1

α + β + γ = 7/1

α + β + γ = 7