Grade 10Algebra

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=

anshooman giri

8 Years agoGrade 10

1 Answer

Arun

8 Years ago

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

⇒ a^{n/n + 1} c^{1/n + 1} + a^{1/n + 1} c^{n/n + 1} + b = 0

⇒ (aⁿ c)^{1/n + 1} + (can)^{1/n + 1} + b = 0

Regards

Arun (askIITians forum expert)

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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=

anshooman giri

1 Answer

Arun

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