Question

If α and β are the zeros of the quadratic polynomial f(t) = t² − 4t + 3, find the value of α⁴β³ + α³β⁴.

Answer 1

From the question, it is given that:

α and β are the roots of the quadratic polynomial f(t) where a = 1, b = −4 and c = 3

Sum of the roots = α + β = `(-b)/a`

= `-((-4))/1`

= 4

Product of the roots = αβ = `c/a`

= `3/1`

= 3

α⁴β³ + α³β⁴

⇒ α³β³ (α +β) 

⇒ (αβ)³ (α +β)

⇒ (3)³ (4) 

⇒ 27 × 4 

⇒ 108