Math

Prove that if the diffrence between the root of the equation ax^2+bx+c=0 is 1, then a=b^2-a^2/4c

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  1. the roots would be
    (-b +√(b^2 - 4ac)/2a and (-b - √(b^2 -4ac)/2a

    we are told that the difference between them is 1
    so,
    (-b+√(b^2-4a))/2a - (-b - √(b^2-4ac)/2a = 1
    2√(b^2-4ac)/2a = 1
    √(b^2 - 4ac) = a
    square both sides
    b^2 - 4ac = a^2
    b^2 - a^2 = 4ac
    divide both sides by 4c and we have our result

    (b^2 - a^2)/4c = a

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