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Question

For what value of a do the roots of the equation 2x2+6x+a=0 satisfy the condition x1x2+x2x1<2?

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Solution

2x2+6x+a=0
Sum of roots=x1+x2=3
Product of roots=x1x2=a2
x1x2+x2x1<2
x21+x22x1x2<2
(x1+x2)22x1x2x1x2<2
9aa2<2
2(9a)a2<0
9aaa<0
2a9a>0
aϵ(,0)(92,)

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