1
Question
If the quadratic equation 2x2−(a3+8a−1)x+a2−4a=0 possesses roots of opposite signs, then a lies in the interval
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Solution
We have,
2x2−(a3+8a−1)x+a2−4a=0
On comparing with general form of Quadratic Equationax2+bx+c=0
We get a=2,b=−(a3+8a−1),c=a2−4a
Given that roots are of opposite signs
Product of roots < 0
⇒caa<0
⇒a2−4a2<0
⇒a(a−4)<0
∴a ϵ (0,4)
We have,
2x2−(a3+8a−1)x+a2−4a=0
On comparing with general form of Quadratic Equationax2+bx+c=0
We get a=2,b=−(a3+8a−1),c=a2−4a
Given that roots are of opposite signs
Product of roots < 0
⇒caa<0
⇒a2−4a2<0
⇒a(a−4)<0
∴a ϵ (0,4)
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