Question

if α and β are the zeros of the quadratic polynomial x ^2- 8 x + K satisfy the relation 2α + 3 β = 20 find k

Answer 1

x² - 8x + k = 0

α + ß = 8 ... (1)
2α + 3ß = 20 ... (2)

Multiply eq 1 by eq 2 and subtract eq (2) from eq (1)

2α + 4ß = 16
-2α - 3ß = - 20

ß = -4

put value of ß in eq 2

2α + 3ß = 20
2α + 3(-4) = 20
2α - 12 = 20
2α = 20 + 12
α = 32/2 = 16

Now αß = c/a
16 × - 4 = K
-64 = k

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Answer 2

-64 is the value of k