If A & B are the roots of the quadratic equation ax^2+bx+c=0, then find the value of A^2-B^2.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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It is given that A and B are the roots of the quadratic equation ax^2 + bx + c = 0.

`A = (-b + sqrt(b^2 - 4ac))/(2a)` and `B = (-b - sqrt(b^2 - 4ac))/(2a)`

A^2 - B^2 = (A - B)(A + B)

=> `((-b + sqrt(b^2 - 4ac))/(2a) - (-b - sqrt(b^2 - 4ac))/(2a))((-b + sqrt(b^2 - 4ac))/(2a) + (-b - sqrt(b^2 - 4ac))/(2a))`

=> `(2*sqrt(b^2 - 4ac)/(2a))(-2*b)`

=> `(-4*b*sqrt(b^2 - 4ac))/(2a)`

=> `(-2*b*sqrt(b^2 - 4ac))/a`

The value of `A^2 - B^2 = (-2*b*sqrt(b^2 - 4ac))/a`

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