GATE CS 2014 Set 1 — Question 5
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
The roots of are real and positive. and are real. Then has
Correct answer
(D) 4 real roots
Solution
Let the roots of the quadratic equation be and .
Given that the roots are real and positive, we have and .The second equation is .
Since , we can rewrite the equation as:Let . The equation becomes , which is identical in form to the original equation. Therefore, the roots for are the same as the roots for the original equation:Substituting back :
Given that the roots are real and positive, we have and .The second equation is .
Since , we can rewrite the equation as:Let . The equation becomes , which is identical in form to the original equation. Therefore, the roots for are the same as the roots for the original equation:Substituting back :
1. or (since )
2. or (since )
Assuming the roots and are distinct (as is implied by the option for 4 roots), we get 4 distinct real roots: .Thus, the equation has 4 real roots.Continue learning with Success Tracker
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