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25 May, 13:37

For what real value of $v$ is $/frac{-21-/sqrt{301}}{10}$ a root of $5x^2+21x+v$?

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  1. 25 May, 16:37
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    v = 7

    is the value for which

    x = (-21 - √301) / 10

    is a solution to the quadratic equation

    5x² + 21x + v = 0

    Step-by-step explanation:

    Given that

    x = (-21 - √301) / 10 ... (1)

    is a root of the quadratic equation

    5x² + 21x + v = 0 ... (2)

    We want to find the value of v foe which the equation is true.

    Consider the quadratic formula

    x = [-b ± √ (b² - 4av) ]/2a ... (3)

    Comparing (3) with (2), notice that

    b = 21

    2a = 10

    => a = 10/2 = 5

    and

    b² - 4av = 301

    => 21² - 4 (5) v = 301

    -20v = 301 - 441

    -20v = - 140

    v = - 140 / (-20)

    v = 7

    That is a = 5, b = 21, and v = 7

    The equation is then

    5x² + 21x + 7 = 0
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