Q.

If the roots of x410x3+37x260x+36=0 are α,α,β,β,(α<β) then 2α+3β-2αβ=

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a

1

b

–4

c

–1

d

4

answer is B.

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Detailed Solution

α,α,β,βarerootsofx410x3+37x260x+36=0α+α+β+β=102(α+β)=10α+β=5(1)α.α.β.β=36(αβ)2=36αβ=6αβ=±(α+β)24αβ=±2524=±1(2)(1)+(2)2α=6α=3or  2α=4α=2(1)(2)2β=4β=2  or2β=6β=3α<βα=2,  β=32α+3β2αβ=2(2)+3(3)2(2)(3)1312=1

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If the roots of x4–10x3+37x2–60x+36=0 are α,α,β,β,(α<β) then 2α+3β-2αβ=