Question

Question: 10
If α and β are the zeroes of the quadratic polynomial

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

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Answer 1

Step-by-step explanation:

hence

α+β = -b/a = -(-4)/1 = 4

and αβ = c/a = 3/1 = 3

hence α = 3/β

putting this value in the 1st eq

we get...

in picture 1

we got β = 3,1

then if taking β = 3 then.

α = 3/3 = 1

hence α^4β^3+α^3β^4 = 1×27+1×81 = 108 answer.

hope it helps you...

Answer 2

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