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

Expert Answers

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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

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