Question

if alfa, beta are zeroes of x2-6x+k. what is the value of k if 3alfa+2beta=20

Answer 1

3alpha + 2beta = 20
2beta = 20 - 3alpha

alpha + beta = -(-6)/1
alpha + beta = 6
(multiplying 2 on both sides)
2alpha + 2beta = 12
2alpha + 20 - 3alpha = 12
-alpha = 12 - 20
apha = 8

alpha × beta = k/1
(multiplying 2 on both sides)
alpha × 2 beta = 2k
alpha(20 - 3 alpha) = 2k
8(20 - 3×8) = 2k
k = 4(20 - 24)
k = 4 × (-4)

*k = -16*

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