 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  As easy as abc (Posted on 2011-06-28) Given an equation ax^2+bx+c=0 what values a,b cause the roots of the equation to be a and b and the discriminant to be equal to c? Comments: ( Back to comment list | You must be logged in to post comments.) My Attempt | Comment 5 of 10 | `Here is my attempt.`
`x=a ==> a*a^2 + b*a + c = 0   (1)`
`x=b ==> a*b^2 + b*b + c = 0   (2)`
`Subtracting (2) from (1) gives`
`a^3 - a*b^2 + b*a - b^2 = 0`
`       or`
`(a-b)*(a^2 + b*a + b) = 0`
`   a^2 + b*a + b = 0  gives`
`           -a^2      b = ------            a+1`
`      b^2 - 4*a*c = c  gives`
`         a^4 - 4*c*a^3 - 9*c*a^2 - 6*c*a - c = 0`
`         a = ??? in terms of c`
`   a-b = 0  gives`
`      b = a`
`      b^2 - 4*a*c = c  gives`
`         a^2 - 4*c*a - c = 0`
`         Therefore,`
`            b = a = 2*c +- sqrt(4*c^2 + c)`
`    `

 Posted by Bractals on 2011-06-30 14:45:27 Please log in:

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