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Sum of the roots of a quadratic with a modulus term

This type of question, asked 3 times: 6 Apr 2023, 28 Jan 2025, 21 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    6 Apr 2023

    74
    The sum of all the roots of the equation ∣x2−8x+15∣−2x+7=0\left| x^{2}- 8x + 15 \right|- 2x + 7 = 0 is:

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  2. Question 2

    28 Jan 2025

    65
    The sum, of the squares of all the roots of the equation x2+∣2x−3∣−4=0x^{2}+ |2x - 3| - 4 = 0, is :

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  3. Question 3

    21 Jan 2026 S1

    69
    The sum of all the roots of the equation (x−1)2−5∣x−1∣+6=0(x - 1)^{2}- 5|x - 1| + 6 = 0, is:

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