Q:
      
      
         
            
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 ?
         
       
      
      
      
          
      
      
          Answer & Explanation
         Answer: B) 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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