Question

if alpha and beta are zeroes of polynomial xsquare_6x+9 find value if 3alpha +2beta=20

Answer 1

let r & s be alpha & beta for ease of typing: 
r + s = 6 
rs = a 
3r + 2s = 20 
-2r - 2s = -12 
r = 8 
s = -2 
a = 8 * -2 = -16 
x^2 - 6x - 16 = 0 
check: 
(x + 2)(x - 8) = 0 
x = -2 , 8 
3(8) + 2(-2) 
= 24 - 4 
= 20

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