If α and β are the zeroes of the polynomial 21x2
– x – 2then find the value of α + β + αβ
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Answer:
-1 / 21
Step-by-step explanation:
21x² – x – 2 = 0
a = 21 , b = -1 , c = -2
21x² – x – 2 = 0
= 21x² – 7x + 6x – 2 = 0
= 7x (3x - 1) + 2 (3x - 1) = 0
= (7x + 2) (3x - 1) = 0
7x + 2 = 0 3x - 1 = 0
7x = -2 3x = 1
x = -2/7 x = 1/3
α = -2 / 7 , β = 1 / 3
α + β = -b / a αβ = c / a
α + β = - (-1) / 21 αβ = -2 / 21
α + β = 1 / 21
α + β + αβ = 1 / 21 + (-2 / 21)
= -1 / 21
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