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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Solution
Let the root of the quadratic equation be a and b . According to given condition , A.M.=a+b2=8⇒a+b=16...(1)G.M.=√ab=5⇒ab=25...(2) Thus the quadratic equation is given by, x2−x(sum of roots)+(product of roots)=0x2−x(a+b)+(ab)=0⇒x2−16x+25=0