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  4. If p and q are two prime numbers whose sum of the squares is an odd integer (p<q) and the roots of the quadratic (2 p +1) x 2+( p + q -7) x -5=0 are equal in magnitude but opposite in sign then | p - q | is equal to

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Q. If $p$ and $q$ are two prime numbers whose sum of the squares is an odd integer $(p
Complex Numbers and Quadratic Equations

Solution:

Since $p$ and $q$ are prime number and $p ^2+ q ^2=$ odd integer and also $p < q$
Hence, $p=2$
$5 x^2+(q-5) x-5=0 $
$\text { S.O.R. }=0 $
$\frac{-(q-5)}{5}=0 \Rightarrow q=5$
$\therefore \quad|p-q|=3$