Question

If α and β are the zeroes of the quadratic polynomial

f(t) = t2 – 4t + 3, find the value of α4β3 + α3β4.​

Answer 1

Solution:

Since, α and β are the zeroes of the quadratic polynomial f(t) = t2 – 4t + 3

So, Sum of the zeroes = α + β = 4

Product of the zeroes = α × β = 3

Now,

α4β3 + α3β4 = α3β3(α + β)

= (3)3(4) = 108

Answer 2

Answer:

Step-by-step explanation:

alpha^4beta^3+alpha^3beta^4

alpha^3beta^3(alpha+beta)

=(alpha beta)^3 (alpha+beta)

alpha+beta=-b/a

                   =-(-4)/1

                   =4

alpha*beta=c/a=3/1=3

so we get

3^3*4

=27*4

=108

hope this helped ;)