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18 October, 02:17

If - 4 is a root of the equation x^2+px-4=0 and the equation x^2+px+q=0 has equal roots, find the value of p and q

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  1. 18 October, 02:40
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    p = 3, q = 2.5

    Step-by-step explanation:

    Given that x = - 4 is a root of the equation, then

    ( - 4) ² - 4p - 4 = 0, that is

    16 - 4p - 4 = 0

    12 - 4p = 0 (subtract 12 from both sides)

    - 4p = - 12 (divide both sides by - 4)

    p = 3

    Also given that the equation x² + px + q = 0 has equal roots

    Thus the value of the discriminant b² - 4ac = 0

    Here a = 1, b = p and c = q, thus

    p² - 4q = 0 ← substitute p = 3 from above into the equation

    9 - 4q = 0 (subtract 9 from both sides)

    - 4q = - 9 (divide both sides by - 4)

    q = 2.5
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