1. Tardigrade
  2. Question
  3. Mathematics
  4. 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 Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Quadratic Equations

Solution:

Given quadratic equation is $x^2-12 x+35$
Here, $\alpha$ and $\beta$ are roots of the given quadratic equation, then
$ \alpha+\beta=10 $
$\alpha \beta=25$
$= 2\left(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\right)=2\left(\frac{\alpha^2+\beta^2}{\alpha \beta}\right) $
$= 2\left(\frac{(\alpha+\beta)^2-2 \alpha \beta}{\alpha \beta}\right)=2\left(\frac{10^2-2 \times 25}{25}\right)$
$= 2\left(\frac{100-50}{25}\right)=2\left(\frac{50}{25}\right)=4$