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One root is a given multiple (ratio) of the other: find the coefficient

The same question, asked 2 times: CDS 1 2017*, CDS 2 2017. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2017

    7
    If one root of (a2−5a+3)x2+(3a−1)x+2=0(a^2 - 5a + 3) x^2 + (3a - 1) x + 2 = 0 is twice the other, then what is the value of 'a' ?

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  2. Question 2

    CDS 2 2017

    5
    What is the positive value of mm for which the roots of the equation 12x2+mx+5=012x^2 + mx + 5 = 0 are in the ratio 3 : 2 ?

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