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If the roots of a quadratic equation ax^2 + bx + c = 0 are of the form X and X^2, what...

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xetaalpha2 | Student | (Level 2) Honors

Posted June 21, 2013 at 4:45 PM via web

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If the roots of a quadratic equation ax^2 + bx + c = 0 are of the form X and X^2, what is the relation between a, b and c.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 21, 2013 at 4:53 PM (Answer #1)

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The roots of a quadratic equation ax^2 + bx + c = 0 are given by `(-b+-sqrt(b^2 - 4ac))/(2a)`

If the roots are of the form X and X^2

`(-b + sqrt(b^2 - 4ac))/(2a) = ((-b-sqrt(b^2 - 4ac))/(2a))^2` if X > 1 and `(-b - sqrt(b^2 - 4ac))/(2a) = ((-b+sqrt(b^2 - 4ac))/(2a))^2` if X < 1

It is not possible to express the relation between the coefficients in a better way.

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