Question

What is the sum of the product of the zeros taken two at a time for f(x) = x^3 − 2x^2 − 7x + 14? plz fast

Answer 1

Answer:

Let the polynomial be ax^3 + bx^2 + cx + d and the zeroes be α, β and γ

Then, α + β + γ = -(-2)/1 = 2 = -b/a αβ + βγ + γα = -7 = -7/1 = c/a αβγ = -14 = -14/1 = -d/a

$\red{ \sf \: ∴ a = 1, b = -2, c = -7 and \: d = 14}$

So, one cubic polynomial which satisfy the given conditions will be

$\sf \: x {}^{3} – 2x {}^{2} – 7x + 14$

Answer 2

Step-by-step explanation:

the sum of the products of the zeros taken two at a time is = (c/a)= -7/1=-7