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Question

If α and β are the zeroes of the polynomial kx2 + 3x + 2 such that α2+β2+αβ=-125, find the value of k.
[Hint: α2+β2+αβ=α+β2-αβ]

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Solution

Hi, kx2+3x+2 = 0 so sum of roots α+β= -coefficient of xcoefficient of x2= -3kproduct of roots αβ = cosntant term coefficient of x2= 2kso here α2+β2+αβ= -125α2+β2+2αβ-αβ= -125α+β2-αβ= -125putting values -3k2-2k= -1259k2-2k= -1259-2kk2= -125225-50k = -k2k2-50k +225 = 0 k2-5k -45k+225 = 0 kk-5-45k-5= 0k-5k-45= 0 k = 5, 45

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