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Question

The quadratic equation ax2+bx+c=0 will always have imaginary root in which of the following cases?

A
a<1, 0<c<1, b>0
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B
a<1, 1<c<0, 0<b<1
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C
a<1, c<0, b>1
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D
a<1, c<1, 1<b<2
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Solution

The correct option is C a<1, c<1, 1<b<2
f(x)=ax2+bx+c=0
Roots are imaginary therefore discriminant is less than zero
b24ac<0
If a>0 so upward parabola and f(x)>0 xR - 1
If a<0 so downward parabola and f(x)<0 xR - 2
As per given options a<-1, condition 2 will be satisfied
b24ac<0 is always positive so ac is also positive as a is negative, C is also negative If c<1,1<b<2
a<1,c<1,1<b<2

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