Question

If α β and ɤ are zeros of the polynomial f(x) =x

3

-3x2+7x-12 then find the value of

(αβ)-1 +(βɤ)

-1 +(ɤα)-1.​

Answer 1

Step-by-step explanation:

Given -

• p(x) = x³ - 3x² + 7x - 12

To Find -

Value of (αβ)-1 + (βγ)-1 + (γα)-1

→ -αβ - βγ - γα

→ -1(αβ + βγ + γα)

As we know that :-

• αβ + βγ + γα = c/a

here,

a = 1

b = -3

c = 7

d = -12

Then, αβ + βγ + γα =

→ 7/1

→ 7

Then,

The value of -1(αβ + βy + yα) is

→ -1(7)

→ -7

Hence,

The value of -1(αβ + βy + yα) is -7.