Question

If α and β are the zeroes of the quadratic polynomial ax²+bx+c, find the value √α/β + √β/α

Answer 1

       a x²  + b x + c

  If α , β  are the roots, then  α + β = - b / a
  α β = c / a
 
$\sqrt{\frac{\alpha}{\beta}}+\sqrt{\frac{\beta}{\alpha}}=\frac{\sqrt{\alpha}\sqrt{\alpha}+\sqrt{\beta\ \beta}}{\sqrt{\alpha\ \beta}}\\\\=\frac{\alpha+\beta}{\sqrt{\alpha\ \beta}}\\\\=\frac{-b}{a}*\frac{1}{\sqrt{c/a}}=-\frac{b\sqrt{a}}{a\sqrt{c}}=-\frac{b}{\sqrt{ac}}$