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Question
Solve the cubic equation: 2x3 – x2 – 18x + 9 = 0 if sum of two of its roots vanishes
Solution
The given equation is 2x3 – x2 – 18x + 9 = 0
`x^3 - x^2/2 - 9x + 9/2` = 0
Let the roots be α, – α, β
`alpha - alpha + beta = - ((-1)/2)`
⇒ `beta = 1/2`
`(alpha)(- alpha) (beta) = (- 9)/2`
⇒ `= alpha^2 (1/2) = (- 9)/2`
α2 = 9
α = ± 3
The roots are 3, `- 3, 1/2`
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