If alpha and beta are the zeros of the polynomial f(x)= x2-4x+3, find the value of alpha4 × beta3 +alpha3 × beta4​

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1. Answer :

   108

   Explanation :

   Given polynomial,

   ⇒ x² – 4x + 3 with zeros α and β

   On comparing with ax² + bx + c

   • a = 1
   • b = -4
   • c = 3

   Then,

   • α + β = -b/a = 4
   • αβ = c/a = 3

   Finding :

   ⇒ α⁴ × β³ + α³ × β⁴

   ⇒ α³β³(α + β)

   ⇒ (αβ)³(α + β)

   On substituting the values,

   ⇒ (3)³(4)

   ⇒ 27 × 4

   ⇒ 108

   Required answer : 108

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