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Grade: 10
        
if one root of the quadratic equation ax^2+bx+c=0 is equal to the nth powe of the other root ,then find the value of (ac^n)1/n+1 + (a^n * c)^1/n+1=
8 months ago

Answers : (1)

Arun
13976 Points
							
Dear student
 
 
Sol. Let α, β be the roots of eq. ax2 + bx + c = 0
 
According to the question,
 
Β = αn
 
Also α + β = -b/a ; αβ = c/a
 
α β = c/a ⇒ α. α n = c/a ⇒ α = (c/a)1/n + 1
 
then α + β = - b/a ⇒ α + αn = -b/a
 
or (c/a)1/n + 1 + (c/a)n/n + 1 = -b/a
 
⇒ a .(c/a)1/n + 1 + a .(c/a)n/n + 1 + b = 0
 
⇒ an/n + 1 c1/n + 1 + a1/n + 1 c n/n + 1 + b = 0
 
⇒ (an c) 1/n + 1 + (can) 1/n + 1 + b = 0
 
 
Regards
Arun (askIITians forum expert)
8 months ago
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