Question

If $a,b,c$ are the roots of $x^3+qx+r=0$, form the equation whose roots are
$k{a}^{-1},k{b}^{-1},k{c}^{-1}$.

Answer 1

$x^3+qx+r=0$

$y=\frac{k}{x}⟹x=\frac{k}{y}\therefore$ replace $x$ with $\frac{k}{y}$ in the given question

$⟹{\left(\frac{k}{y}\right)}^3+q\left(\frac{k}{y}\right)+r=0$

$⟹k^3+qk{y}^2+r{y}^3=0$

$⟹r{y}^3+qk{y}^2+k^3=0$