Mathematics

Question

p= -5x2 + 70x - 165​

1 Answer

  • For this case we have the following quadratic equation:

    [tex]p = -5x ^ 2 + 70x-165[/tex]

    To find the roots, we equal 0.

    [tex]-5x ^ 2 + 70x-165 = 0[/tex]

    Where:

    [tex]a = -5\\b = 70\\c = -165[/tex]

    The solution will be given by:

    [tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

    Substituting we have:

    [tex]x = \frac {-70 \pm \sqrt {70 ^ 2-4 (-5) (- 165)}} {2 (-5)}\\x = \frac {-70 \pm \sqrt {4900-3300}} {- 10}\\x = \frac {-70 \pm \sqrt {1600}} {- 10}\\x = \frac {-70 \pm40} {- 10}\\x = - (-7\pm4)[/tex]

    We have two roots:

    [tex]x_ {1} = 7-4 = 3\\x_ {2} = 7 + 4 = 11[/tex]

    Answer:

    [tex]x_ {1} = 3\\x_ {2} = 11[/tex]

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