Let a,b,c,a1,b1,c1,∈R and ax2+bx+c>0∀x∈R and a1x2+b1x+c1>0∀x∈R. 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∀x∈R a1x2b1x+c1>0∀x∈R So, b2−4ac<0,a>0,c>0 and b21−4a1c1<0,a1>0,c1>0 b2<4ac and b21<4a1c1 b2b21<16a1c1ac (bb1)2−4a1acc1<12a1ac.c1 (positive) b2b21−4aa1cc1 is discriminate of aa1x2+bb1x+cc1=0 If may be negative, zero, or positive that way we can't say nature of the root.