Question

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

Answer 1

Let the required roots be a and b.
Then, `AM=(a+b)/2 rArr (a+b)/2=8 rArr a+b=16` ...(i)
and `GM=sqrt(ab) rArr sqrt(ab)=5 rArr ab=25` ...(ii)
`:.` sum of roots =16 and product of roots `=25`
Hence, the required equation is `x^(2)-16x+25=0`.