Consider the equation log 2(x2-5 x+5) ⋅ log 5( log 2((x+3) x+4))=0 whose roots are α, β, γ and δ, where α

Question

Consider the equation log 2(x2-5 x+5) ⋅ log 5( log 2((x+3) x+4))=0 whose roots are α, β, &gamma; and δ, where α<β<&gamma;<δ. The quadratic equation whose roots are α+β and &gamma;+δ is (A) x2-2 x-15=0 (B) x2-3 x+10=0 (C) x2-5 x+10=0 (D) x2+2 x-15=0

Tardigrade Admin · Accepted Answer

log 2(x2-5 x+5) ⋅ log 5( log 2((x+3) x+4))=0 log 2(x2-5 x+5)=0 OR log 5( log 2((x+3) x+4))=0 ⇒ x2-5 x+5=1 ⇒ log 2((x+3) x+4)=1 ⇒ x2-5 x+4=0 ⇒ x2+3 x+4=2 ⇒ x=1,4 ⇒ x2+3 x+2=0 ⇒ x=-1,-2 ∴ α=-2, β=-1, &gamma;=1, δ=4 α+β=-3, &gamma;+δ=5 ∴ quadratic equation whose roots are α+β and &gamma;+δ, is x2-2 x-15=0

Q. Consider the equation $lo g_{2} (x^{2} - 5 x + 5) \cdot lo g_{5} (lo g_{2} ((x + 3) x + 4)) = 0$ whose roots are $α, β, γ$ and $δ$ , where $α < β < γ < δ$ .
The quadratic equation whose roots are $α + β$ and $γ + δ$ is

$x^{2} - 2 x - 15 = 0$

$x^{2} - 3 x + 10 = 0$

$x^{2} - 5 x + 10 = 0$

$x^{2} + 2 x - 15 = 0$

Q. Consider the equation log2​(x2−5x+5)⋅log5​(log2​((x+3)x+4))=0 whose roots are α,β,γ and δ, where α<β<γ<δ. The quadratic equation whose roots are α+β and γ+δ is

x2−2x−15=0

x2−3x+10=0

x2−5x+10=0

x2+2x−15=0

Q. Consider the equation $lo g_{2} (x^{2} - 5 x + 5) \cdot lo g_{5} (lo g_{2} ((x + 3) x + 4)) = 0$ whose roots are $α, β, γ$ and $δ$ , where $α < β < γ < δ$ .
The quadratic equation whose roots are $α + β$ and $γ + δ$ is

$x^{2} - 2 x - 15 = 0$

$x^{2} - 3 x + 10 = 0$

$x^{2} - 5 x + 10 = 0$

$x^{2} + 2 x - 15 = 0$