Question

Find m so that the difference between the roots of the quadratic equation x2 - 2x + m = 0 is 3.
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Answer 1

Let the two roots of the equation be p and q.

pq = m/1 = m

Conversely, m = pq

p-q = 3 ....... (i)

p+q = -(-2/1) = 2 ........ (ii)

p-q+p+q = 3+2

or, 2p = 5

or, p = 5/2

Therefore, putting the value of p in equation (i) we get :

5/2 - q = 3

or, 5/2 - 3 = q

or, q = - 1/2

Now, m = pq

so, m = 5/2 × (-1/2) [Putting the values of p and q]

or, m = - 5/4 (Ans.)