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The sum of the three numbers in AP is 3 and their products is -35. Find the numbers.

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An important question from ML Agarwal of Class10 for board examination We have asked The sum of the three numbers in AP is 3 and their products is -35. Find the numbers.
ML Publication, Class 10, Arithmetic Progression Chapter 9 question no 22

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  1. Let three no’s in AP be a−d,a,a+d
    Given, sum of three numbers =−3
    Therefore, a−d+a+a+d=−3
    ⇒3a=−3
    ⇒a=−1
    Also product of three numbers =8
    Therefore, (a−d)a(a+d)=8
    ⇒a(a2−d2)=8
    ⇒(−1)(1−d2)=8
    ⇒1−d2=−8
    ⇒d2=9
    ⇒d=3 and d=−3
    If a=−1 and d=3

    numbers are −4,−1,2.
    And if a=−1 and d=−3

    numbers are 2,−1,−4.

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