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Grade: 11
        
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????????
7 months ago

Answers : (2)

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