If the roots of the quadratic equation are α and β, then its equation can be written as (x-α)(x-β)=0 i.e. x2-x(α+β)+α β=0 For given quadratic equation x2-10 x+25=0, find: 2((α/β)+(β/α))

Question

If the roots of the quadratic equation are α and β, then its equation can be written as (x-α)(x-β)=0 i.e. x2-x(α+β)+α β=0 For given quadratic equation x2-10 x+25=0, find: 2((α/β)+(β/α)) (A) (10/3) (B) 4 (C) (88/5) (D) 9

Tardigrade Admin · Accepted Answer

Given quadratic equation is x2-12 x+35 Here, α and β are roots of the given quadratic equation, then α+β=10 α β=25 = 2((α/β)+(β/α))=2((α2+β2/α β)) = 2(((α+β)2-2 α β/α β))=2((102-2 × 25/25)) = 2((100-50/25))=2((50/25))=4

Q. If the roots of the quadratic equation are $α$ and $β$ , then its equation can be written as $(x - α) (x - β) = 0$ i.e. $x^{2} - x (α + β) + α β = 0$
For given quadratic equation $x^{2} - 10 x + 25 = 0$ , find:
$2 (\frac{α}{β} + \frac{β}{α})$

$\frac{10}{3}$

4

$\frac{88}{5}$

9

Q. If the roots of the quadratic equation are α and β, then its equation can be written as (x−α)(x−β)=0 i.e. x2−x(α+β)+αβ=0 For given quadratic equation x2−10x+25=0, find: 2(βα​+αβ​)

310​

4

588​

9

Given quadratic equation is x2−12x+35 Here, α and β are roots of the given quadratic equation, then α+β=10 αβ=25 =2(βα​+αβ​)=2(αβα2+β2​) =2(αβ(α+β)2−2αβ​)=2(25102−2×25​) =2(25100−50​)=2(2550​)=4

Q. If the roots of the quadratic equation are $α$ and $β$ , then its equation can be written as $(x - α) (x - β) = 0$ i.e. $x^{2} - x (α + β) + α β = 0$
For given quadratic equation $x^{2} - 10 x + 25 = 0$ , find:
$2 (\frac{α}{β} + \frac{β}{α})$

$\frac{10}{3}$

$\frac{88}{5}$