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Question

If α,β are the roots of the equation x2+x+3=0, then the equation 3x2+5x+3=0 has root

A
αβ
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B
βα
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C
αβ+βα
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D
none of these
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Solution

The correct options are
A αβ
B βα
Considering
x2+x+3=0
α+β=1
And α.β=3
Now
α2+β2=12(3)
=5
Hence,
α2+β2α.β=αβ+βα=53
Let
αβ=α
and βα=β
Hence,
(xα)(xβ)=0 be a quadratic equation.
x2(α+β)+α.β=0
Substituting the value of roots we get
x25x3+1=0
3x2+5x+3=0

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