Question

if one root of quadratic equation lx2+mx+n=0 is double the other. find the condition

Answer 1

Let α is one root of given equation lx² + mx + n = 0 , then other roots will be 2α.
as you know,
sum of roots = - coefficient of x/coefficient of x²
α + 2α = -m/l
α = -m/3l -------(2)

product of roots = constant/coefficient of x²
α.2α = n/l ⇒ α² = n/2l -----(2)

From equation (1) and (2) ,
(-m/3l)² = n/2l
⇒m²/9l² = n/2l
⇒ 2m² = 9nl

Hence, condition is $\boxed{\boxed{\bold{2m^2=9nl}}}$

Answer 2

hope this will help you