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vinita sharma Grade:
        

I have problem in this question So plz solve this asap !!!!!!!


If p and q are the roots of the equation x2 - bx + c = 0, then what is the equation if the roots are (pq + p + q) and (pq - p - q)?


 

8 years ago

Answers : (1)

vijay narang
27 Points
										

I solve this question here ...this question is simple !!!


explanation:


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



=> x2 - 2cx + c2 - b2 = 0

8 years ago
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