Question

If α, β, γ are the zeros of the polynomial x³ – 6x² – x + 30 then the value of (αβ + βy + γα) is ______.

Options

• –1

• 1

• –5

• 30

Answer 1

If α, β, γ are the zeros of the polynomial x³ – 6x² – x + 30 then the value of (αβ + βy + γα) is –1.

Explanation:

For a cubic ax³ + bx² + cx + d.

Vieta’s formula gives `αβ + βγ + γα = c/a`. 

Here, a = 1 and c = –1.

So, αβ + βγ + γα = –1.