Given, α and β are zeroes of the quadratic polynomial 𝑥² − 6𝑥 + 𝑎

Now, α + β = 6 ......1

Given, 3𝛼 + 2𝛽 = 20  ........2

Multiply by 3 in equation 1, we get

3α + 3β = 18 ......3

Subtract equation 2 and 3, we get

     (3α + 2β) - (3α + 3β) = 20 - 18

=> 3α + 2β - 3α - 3β = 2

=> -β = 2

=> β = -2

From equation 1, we get

     α + (-2) = 6

=> α - 2 = 6

=> α = 6 + 2

=> α = 8

Now, product of the zeroes = a/1

=> 8 * (-2) = a

=> a = -16

So, the value of a is -16