Let 
and 
be two quadratic polynomials with real coefficients and satisfy 
. Then which of the following is (are) correct?
or 
must have real roots. 
or 
must have real roots. 
and 
must have real roots. 
and 
must have imaginary roots.
Text Solution
Verified by ExpertsB
Let's carefully check.
Given:
We want statements about real roots.
Step 1: Real roots condition
real 
real 
Step 2: Check implication of 
Rewrite:
If both f and g have negative discriminants, then 
and 
Then 
and 
Sum: 
(AM-GM inequality)
So both discriminants cannot be negative.
Therefore at least one quadratic must have real roots.
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