if the roots of the equation ` z^(2) + ( p +iq) z + r + is =0` are real wher p,q,r,s, `in` ,R , then determine ` s^(2) + q^(2)r`.

Explanation

Let ` x in ` R be a root of the given equation.
` Rightarrow x^(2) = ( p +iq) x + r + is =0`
` Rightarrow (x^(2) + px+r)+ i(qx + s) = 0=0+ I.0`
Equating real and imaginary parts form respective sides we gets `x^(2)+ px + r =0 and qx + s =0 Rightarrow x = - s/q`
Sustituting for x in the first relation, we have .
` s^(2)/q^(2) - (ps)/q + r =0`
` Rightarrow (s^(2) +q^(2)r) = pqs`