Question

Find the polynomial equation whose roots are the reciprocals of the roots $x^4-3x^3+7x^2+5x-2=0$

Answer 1

put $x=\frac{1}{x}$ in the given equation

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

Therefore required equation is $2x^4-5x^3-7x^2+3x-1=0$