write down the roots of a quadratic equation lx²+mx+n=0
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Step-by-step explanation:
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}}}
2m
2
=9nl
Answered by
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Answer:
Given,
β=2α one root is the double of other root of the equation lx
2
+mx+n=0
x
2
−(α+2α)x+(α)(2α)=0
x
2
−3αx+2α
2
=0
comparing the equations, we get,
l=1
m=−3α⇒α=−
3
m
n=2α
2
n=2(−
3
m
)
2
∴n=
9
2
m
2
Is the required condition.
Step-by-step explanation:
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