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Suppose that the coefficient of the quadratic term and the coefficient of the linear term of a quadratic are equal. If the quadratic has a double root, what is the ratio of the coefficient of the quadratic term to the constant term?

 May 24, 2021
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The quadratic is ax^2+ax+b and for this to be a perfect square, it must be (sqrtax+sqrtb)^2 which is ax^2+b+2sqrt(ab)x so we have 2sqrtab=a which means 4ab=a^2 so a/b = 4.

 May 25, 2021

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