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Question

Let a,b,c,a1,b1,c1,R and ax2+bx+c>0 xR and a1x2+b1x+c1>0 xR. Then

A
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B
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C
will have real roots.
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D
Nothing can be said in general about the nature of roots of,
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Solution

The correct option is D Nothing can be said in general about the nature of roots of,
Solution : We have ax2+bx+c>0 xR
a1x2b1x+c1>0 xR
So, b24ac<0,a>0,c>0
and b214a1c1<0,a1>0,c1>0
b2<4ac and b21<4a1c1
b2b21<16a1c1ac
(bb1)24a1acc1<12a1ac.c1 (positive)
b2b214aa1cc1 is discriminate of aa1x2+bb1x+cc1=0
If may be negative, zero, or positive that way we can't say nature of the root.

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