Question

If ‘α’ and ‘β’ are the zeroes of the polynomial p(y) = y² − 5y + 3, then find the value of α⁴β³ + α³β⁴. 

Answer 1

Given:

p(y) = y² − 5y + 3

To Find:

`α^4β^3 + α^3β^4`

Formula:

Sum of the zeroes: α + β

Product of the zeroes: αβ

Solution:

p(y) = y² − 5y + 3

∴ a = 1, b = −5 and c = 3

α + β = `-b/a = (-(-5))/1 = 5`       ...(i)

αβ = `c/a = 3/1 = 3`          ...(ii)

`α^4β^3 + α^3β^4`

= `α^3β^3(α + β)`

= `(αβ)^3(α + β)`

= `(3)^3(5)`          ...[By substituting (i) and (ii) we get]

= 27 × 5

= 135