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 ?a)55b)56c)60d)64Correct answer is option 'B'. Can you explain this answer?

Question

If p and q are the roots of the equation x2 &ndash; 15x + r = 0 and p &ndash; q = 1, then what is the value of r ?a)55b)56c)60d)64Correct answer is option 'B'. Can you explain this answer?

Answer

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 = 15² – 1
p2 + q2 + 2pq – p2 – q2 +2pq = 225 -1
4pq = 224
4r = 224
r = 56

Answer

+ bx + c = 0, then the equation can be written as:

(x - p)(x - q) = 0

Expanding this expression gives:

x^2 - (p + q)x + pq = 0

Comparing this with the original equation x^2 + bx + c = 0, we can see that:

b = -(p + q)
c = pq

Therefore, the sum of the roots (p + q) is equal to -b and the product of the roots (pq) is equal to c.

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