Respuesta :

carlosego

For this case we have a quadratic equation of the form:

[tex]ax ^ 2 + bx + c = 0\\x ^ 2 + 11x-4 = 0[/tex]

Where:

[tex]a = 1\\b = 11\\c = -4[/tex]

We find the roots:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\x = \frac {-11 \pm \sqrt {11 ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {-11 \pm \sqrt {121 + 16}} {2}\\x = \frac {-11 \pm \sqrt {137}} {2}[/tex]

The roots are:

[tex]x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}[/tex]

Answer:

[tex]x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}[/tex]

kudzordzifrancis

ANSWER

[tex]x = - \sqrt{ 7}i \: \: or \: \: x = + \sqrt{ 7}i[/tex]

EXPLANATION

The given expression is

[tex] {x}^{2} = - 11 + 4[/tex]

Simplify the left hand side to get:

[tex] {x}^{2} = - 7[/tex]

Take square root

[tex]x = \pm \sqrt{ - 7} [/tex]

[tex]x = \pm \sqrt{ 7} \times \sqrt{ - 1} [/tex]

Note that:

[tex] {i}^{2} = - 1 \implies \sqrt{ - 1} = i[/tex]

[tex]x = \pm \sqrt{ 7}i[/tex]

Split the plus or minus sign

[tex]x = - \sqrt{ 7}i \: \: or \: \: x = + \sqrt{ 7}i[/tex]

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