Question

If one root of the quadratic equation lx^2+mx+n=0 is double the other find the condition

Answer 1

let the roots be α,β
and α=2β
so sum of the roots = -b/a
α+β = -m/l
3β = -m/l
β = -m/3l
and products of roots are c/a
α*β = n/l
3β² = n/l
β²= n/3l
so
(-m/3l)²= n/3l
m²/9l²= n/3l
m²/3l = n
m²= 3nl

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