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If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?

Correct Answer: 56

Explanation:

In the below equation,


x2–15x + r = 0


sum of roots = p + q = -(-15)/1 = 15 (sum of roots for equation ax2+ bx + c is -b/a)


product of roots = pq = r/1 = r     (product of roots for equation ax2+ bx + c is c/a)


given p –q = 1


also we know that p+q = 15


subtracting the squares of both


(p+q)2 + (p-q)2 = 15^2–1


p2 + q2 + 2pq –p2 –q2 +2pq = 225 -1


4pq = 224


4r = 224


r = 56


 


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