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f(x)=x^2-(m-3)x+m=0 is a quadratic equat...

f(x)=`x^2-(m-3)x+m`=0 is a quadratic equation, find values of m for which
both roots are positive

Text Solution

Verified by Experts

`D=(m-3)^2-4m=m^2-10m+9gt0 forall m in(-infty,1) cup(9,infty)`
Let `alpha,beta` be the roots.
`Dge0,alpha+betagt0,alphabetagt0`
`implies m-3gt0, mgt0 "so m" in[9,infty)`
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