Question

Form an equation whose roots are the reciprocals of the roots of x^4-5x^3+7x^2-3x+6=0

Answer 1

Put $\frac{1}{x}$ in the given equation

$\frac{1}{x^4}-\frac{5}{x^3}+\frac{7}{x^2}-\frac{3}{x}+6=0$

$\frac{1-5x+7x^2-3x^3+6x^4}{x^4}=0$

$6x^4-3x^3+7x^2-5x+1=0$