without solving quadratic equation for what value of " m" are the roots of (3m+1)x^2+(11+m)x+9=0 equal?
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Condition for getting roots equal is that discriminant should be equal to 0
therefore,
b²-4ac=0
=>(11+m)²-4×(3m+1)×9=0
=>121+m²+22m-4×(27m+9)=0
=>121+m²+22m-108m-36=0
=>m²-86m+85=0
=>m²-m-85m+85=0
=>m(m-1)-85(m-1)=0
=>(m-85)(m-1)=0
=>m=1 or 85
therefore,
possible values of m are 1 and 85
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