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        if p,q,r,s are positive integers such that the arthemetic mean of the roots of the equation x^2-px+q^2 and the geometric mean of the roots of the equationx^2-rx+s^2  are equal, then the values of ,q,r,s can be????????
2 years ago

Rohit Kumar
20 Points
							Roots of  $x^2-px+q^2=0$ are $\frac{p+\sqrt(p^2-4q^2)}{2}$ and $\frac{p-\sqrt(p^2-4q^2)}{2}$ . Arithemetic mean of the roots is $\frac{p}{2}$.Roots of  $x^2-rx+s^2=0$ are $\frac{r+\sqrt(r^2-4s^2)}{2}$ and $\frac{r-\sqrt(r^2-4s^2)}{2}$ . Geometric mean of the roots is $s$.By given condition  A.M. = G.M. this implies $p = 2.s$ .So we can take any integer value of $q,r,s$ and value of $p$ = 2*value of $s$.

one year ago
Rohit Kumar
20 Points
							Correction in final answer : .$s$ = 2*value of $p$ and value of $q,r,s$So we can take any positive integer value of

one year ago
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• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions