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Question
The value of a for which the quadratic equation 2x^2 - (a^3+8a-1)X + a^2-4a =0 possess roots of opposite signs are given by
a>0
a>5
4<a<8.5
0<a<4
The value of a for which the quadratic equation 2x^2 - (a^3+8a-1)X + a^2-4a =0 possess roots of opposite signs are given by
a>0
a>5
4<a<8.5
0<a<4
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Solution
Roots are oppsite if product of roots is negattive
and product of roots is (a^2-4a)/2 < 0
a^2-4a < 0
a(a-4) < 0
0 < a < 4
and product of roots is (a^2-4a)/2 < 0
a^2-4a < 0
a(a-4) < 0
0 < a < 4
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