If α≠β but, α^2=4α-2 and β^2=4β-2, then the quadratic equation with roots (α)/(β) and (β)/(α) is

Question

MARKS Content Team · Accepted Answer

Correct answer: (B) x^2-6x+1=0. Since, α^2=4α-2,β^2=4β-2 ⇒ α,β are the roots of x^2=4x-2 ⇒ α+β=4,αβ=2 The quadratic equation with roots (α)/(β),(β)/(α) is, x^2-(α)/(β)+(β)/(α)x+(α)/(β)×(β)/(α)=0 ⇒ x^2-((α+β)^2-2αβ)/(αβ)x+1=0 ⇒ x^2-((16-4))/2x+1=0 ⇒ x^2-6x+1=0

If $α \neq β$ but, $α^{2} = 4 α - 2$ and $β^{2} = 4 β - 2$ , then the quadratic equation with roots $\frac{α}{β}$ and $\frac{β}{α}$ is

Solution

More Quadratic Equation Questions

If α≠β but, α2=4α-2 and β2=4β-2, then the quadratic equation with roots αβ and βα is

Solution

More Quadratic Equation Questions

If $α \neq β$ but, $α^{2} = 4 α - 2$ and $β^{2} = 4 β - 2$ , then the quadratic equation with roots $\frac{α}{β}$ and $\frac{β}{α}$ is