Question

$x {}^{2} - pq + q = 0$
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Answer 1

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x2+px+q=0  ----    (1)

x2+qx+p=0  ----   (2)

By applying mathematical generality 

x=1 is  one of the roots, 

From which both equations, we get

1+p+q=0

from equation 1

products of roots =q

Hence, roots of first equation x=1  and x=q

Similarly, for equation (2)

x=1 and x=p

the equation having roots p and q is 

x2−(p+q)x+pq=0

On substituting the values 

x2+x+pq=0