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# Solve for x: x³ - 5 x² - 2 x + 24 = 0. given that product of two roots is 12.?

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- Pramod KumarLv 78 months ago
Let the roots be α, β, γ. then --

α + β + γ = 5, α β + β γ + α γ = - 2, α β γ = - 24 and α β = 12 (given)

hence γ = - 2,

=> α + β - 2 = 5 ........... => α + β = 7

We know that ( α - β )² = ( α + β )² - 4 α β

=> ( α - β )² = ( 7 )² - 4 (12) = 1

=> ( α - β ) = ± 1

Hence α = 4 , β = 3, Or α = 3 , β = 4

Hence the roots are 4, 3, -2 ............. Answer

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