Question

If a, b, c are zeroes of p(x) = x3 – 3x2+ 4x – 6, then ab + bc + ca =​

Answer 1

Given,

a, b, and c are zeroes of given polynomial, P(x) = x³ - 3x² + 4x - 6.

To find,

value of ab + bc + ca

we know,

if α, β and γ are zeroes of a cubic polynomial

then polynomial is written as,

x³ - (α + β + γ)x² + (αβ + βγ + γα)x - αβγ

on comparing with polynomial p(x) we get,

αβ + βγ + γα = 4

but in question, a , b and c are zeroes so we have to put α = a , β = b and γ = c

therefore, αβ + βγ + γα = ab + bc + ca = 4.