If p and q are the roots of the equation x2 - bx + c = 0, what is the equation if the roots are (pq + p + q) and (pq - p - q)?
Pick one.
A) x2 - 2cx + (c2 - b2) = 0
B) x2 - 2bx + (b2 + c2) = 0
C) bcx2 - 2(b + c)x + c2 = 0
D) x2 + 2bx - (c2 - b2) = 0
E) None
Explanatory Answer   In the given quadratic equation x2 - bx + c = 0,   The sum of the roots p + q = b --- (1)   And the product of the roots pq = c --- (2)   We have to formulate a quadratic equation whose roots are (pq + p + q) and (pq - p - q).   The sum of the two roots = pq + p +q + pq - p - q = 2pq   But from eqn (2), we know that pq = c   Therefore, the sum of the roots = 2c   The product of the roots = (pq + p + q)(pq - p - q)= (pq)2 - (p+q)2   From equation (1) and (2), we know that pq = c and p + q = b   Therefore, the product of the roots = c2 - b2   We know the sum of the roots and the product of the roots.   Therefore, the quadratic equation is x2 - (sum of the roots)x + product of the roots = 0   =&gt; x2 - 2cx + c2 - b2 = 0   x2 - 2cx + (c2 - b2) +  2 -  2= 
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0   x2 - 2cx + (c2 - b2) = 0nswer x2 - 2cx + (c2 - b2) + ( 2 -  2)= 
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0nswer x2 - 2cx + (c2 - b2) = 0+ ( 2 -  2)= 
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If p and q are the roots of the equation x2 - bx + c = 0, what is the equation if the roots are (pq + p + q) and (pq - p - q)?