Question

if one zero of cubic polymonial px^3+qx^2+rx+s then the sqare of the difference of other two zeroes is​

Answer 1

Zeros: x, p, 2

Sum of zeros = $x+p+2=\frac{-q}{p}$; find $(x-p)^2$

P of zeros = $2*x*p=\frac{-s}{p}$

$x+p=\frac{-q}{p}-2; 2xp=\frac{-s}{p}$

$(x+p)^2=(\frac{-q}{p},-2)^2=\frac{q^2}{p^2}+4+\frac{2q}{p}$

$(x-p)^2=\frac{-q}{p^2}+4+\frac{2q}{p^2}-(\frac{-2s}{p})$

$(x-p)^2=\frac{q^2+4p^2+4+25p}{p^2}$