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Question

If 1,α,α are the roots of the equation x36x2+9x4=0, then find the value of α.

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Solution

Fact: If α,β,γ are the roots of cubic equation ax3+bx2+cx+d=0, then
α+β+γ=ba

Thus if 1,α,α are the roots of x36x2+9x4=0, then
1+α+α=61=6
2α=5
α=52

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