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Rajan@2021
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Guru

Find the values of a and b for which x=3/4 and x=-2 are the roots of the equation ax²+bx-6=0

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This question is taken from quadratic equation chapter in which we have given an equation ax²+bx-6=0 and we have to find the value of a and b if the roots of the given equation are 3/4 and -2.

Kindly solve the above problem in detail

RS Aggarwal, Class 10, chapter 4A, question no 3(ii)

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1 Answer

  1. The quadratic equation is a+bx6=0  ……(i)

    Given, x=3/4 and x=2 are the roots of the quadratic equation.
    Thus, putting x=3/4 in equation (i) we get,
    a(3/4+b×3/46=0
    ⇒a×9​/16+3/4b6=0
    ⇒(9a+12b96)​/16=0
    9a+12b96=0
    3a+4b32=0 ….(ii)
    Now, putting x=2 in equation (i), we get
    a(2+b(2)6=0
    4a2b6=0
    2a−b3=0  ….(iii)
    Now, multiplying equation (iii) by 4, we get
    8a4b12=0  ….(iv)
    Now, adding (ii) and (iv), we get
    11a44=0
    ⇒a=44/11
    ⇒a=4
    Now, putting the value of p in equation (iii), we get
    2a−b3=0
    2×4−b3=0
    8−b3=0
    −b=38
    −b=5
    ⇒b=5

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