The roots of ax^2+bx+c=0 are r and s. For the roots of x^2+px+q=0 to be r^2 and s^2, p must be equal to
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for equation first
r+s=-b/a---------(1)
rs=c/a---------(2)
and for second equation
r^2+s^2=-p------(3)
(rs)^2=q
now
r^2+s^2=(r+s)^2-2rs=(-b/a)^2-2c/a=-p
=>( b^2-2ac)/a^2=-p
=> p=(2ac-p^2)/a^2
r+s=-b/a---------(1)
rs=c/a---------(2)
and for second equation
r^2+s^2=-p------(3)
(rs)^2=q
now
r^2+s^2=(r+s)^2-2rs=(-b/a)^2-2c/a=-p
=>( b^2-2ac)/a^2=-p
=> p=(2ac-p^2)/a^2
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