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  • If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation

32.   If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation

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Let roots of the quadratic equation be a and b.

According to given condition,

               AM=\frac{a+b}{2}=8

                \Rightarrow (a+b)=16

                GM=\sqrt{ab}=5 

                 \Rightarrow ab=25

We know that   x^2-x(sum\, of\, roots)+(product\, of\, roots)=0

                   x^2-x(16)+(25)=0

                  x^2-16x+25=0

Thus, the quadratic equation = x^2-16x+25=0

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