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Question

Let a,b,c be real numbers such that a+b+c<0 and the quadratic equation ax2+bx+c=0 has imaginary roots. Then

A
a<0,c<0
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B
a>0,c<0
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C
a<0,c>0
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D
a>0,c>0
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Solution

The correct option is A a<0,c<0
ax2+bx+c=0 has imaginary roots
f(x)=ax2+bx+c does not intersect x-axis for any real x. Thus, its graph is either an upward opening parabola lying completely above the x-axis or its a downward opening parabola lying completely below the x-axis.

Since, f(1)=a+b+c<0.
So, it lies completely below the x-axis.
a<0
Also D<0
b24ac<0
b2<4ac
a and c will have the same sign.

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