if alpha and beta are the zeroes of the polynomial 3x2-2x-7 then find value of alpha/beta+beta/alpha - Maths - Polynomials

Question

if alpha and beta are the zeroes of the polynomial
3x2-2x-7 then find value of alpha/beta+beta/alpha

Manbar Singh · Accepted Answer

The given polynomial is, px = 3x2 - 2x - 7 Since α and β
are zeroes of px, thenα + β = - coefficient of
xcoefficient of x2 = - -23 = 23α × β = constant
termcoefficient of x2 = -73now,αβ + βα =
α2+β2α × β = α + β2 -
2αβαβ⇒αβ + βα = 2/32
- 2 × -73-73⇒αβ + βα =49+143-73 =
46/9-7/3 = - 4621