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 (1/α)+(1/β)

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 (1/α)+(1/β) (A) (2/5) (B) (4/5) (C) (5/2) (D) (2/3)

Tardigrade Admin · Accepted Answer

Given quadratic equation is x2-10 x+25 α+β=10 α β=25 Now, (1/α)+(1/β)=((α+β/α β)) (α+β/α β)=(10/25)=(2/5)

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. $x^{2} - x (α + β) + α β = 0$
$\frac{1}{α} + \frac{1}{β}$

$\frac{2}{5}$

$\frac{4}{5}$

$\frac{5}{2}$

$\frac{2}{3}$

Given quadratic equation is $x^{2} - 10 x + 25$
$α + β = 10$
$α β = 25$
Now, $\frac{1}{α} + \frac{1}{β} = (\frac{α + β}{α β})$
$\frac{α + β}{α β} = \frac{10}{25} = \frac{2}{5}$

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 α1​+β1​

52​

54​

25​

32​