Find the product of roots of quadratic equation if |x1-x2|=1 and x^2=2x-m.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The roots of the quadratic equation are x1 and x2. |x1 - x2| = 1 and x^2 = 2x - m

As x^2 = 2x - m

x1^2 = 2* x1 - m

x2^2 = 2*x2 - m

Subtracting the two we get

x1^2 - x2^2 = 2( x1 - x2)

=> (x1 - x2)(x1+ x2) = 2(x1 - x2)

=> x1 + x2 = 2

|x1 - x2| = 1

=> x1 - x2 = 1 or x1 - x2 = -1

=> (x1 - x2)^2 = 1

=> x1^2 + x2^2 - 2x1*x2 = 1...(1)

x1 + x2 = 2

=> x1^2 + x2^2 + 2x1*x2 = 4...(2)

(2) - (1)

=> 4x1*x2 = 3

=> x1* x2 = 3/4

The required product is 3/4

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial