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Question

The value of ′a′ for which the quadratic equation 2x2−x(a2+8a−1)+a2−4a=0 has roots opposite signs, lie in the interval

A
1<a<5
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B
0<a<4
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C
1<a<2
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D
2<a<6
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Solution

The correct option is B 0<a<4
R.E.F image
Given equation is : 2x2x(a2+8a1)+a24a=0
Comparing it with the equation : ax2+bx+c=0
we have a=2
b=(a2+8a1)
c=a24a
For the roots to have opposite signs.
product of roots <0
ca<0
a24a2<0
a24a<0
a(a4)<0
(a0)(a4)<0
aE(0,4)

1177711_1034389_ans_da1477a90d8e47c7aedafa3159ccd581.jpg

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