If x⁴ – 5x³ + 9x² – 7x + 2 = 0 has a multiple root of order 3 then the roots are

f(x) = 0 ; f¹(x) = 0 ; f¹¹(x) = 0 have same root ;
$$\begin{gathered} f\left(x\right)=x^4-5x^3+9x^2-7x+2 \\ f\text{'}\left(x\right)=4x^3-15x^2+18x-7 \\ f\text{'}\text{'}\left(x\right)=12x^2-30x+18=0\Rightarrow f\left(1\right)=0,f\text{'}\left(1\right)=0,f\text{'}\text{'}\left(1\right)=0 \end{gathered}$$

$\Rightarrow$1 is the multiple root of order 3 and the other root is 2