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Nookie1986 [14]
4 years ago
7

Factor the expression over the complex numbers. x2+50

Mathematics
2 answers:
Leto [7]4 years ago
8 0

  x² + 50

= x² - (-50)

= \sqrt{x^{2} } +/- \sqrt{-50}            Side note: \sqrt{-50} = \sqrt{(-1) * 5 * 5} = 5i

= (x + 5i)(x - 5i)

Valentin [98]4 years ago
7 0

Answer:

(x+5i\sqrt 2)(x-5i\sqrt 2)

Step-by-step explanation:

We are given that an expression

x^2+50

We have to find the factor of given expression over the complex numbers.

Quadratic formula  fro quadratic equation :ax^2+bx+c=0

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Using the formula

x=\frac{0\pm\sqrt{0-4(50)(1)}}{2}=\frac{\pm i \sqrt{200}}{2}

x=\frac{10i\sqrt 2}{2}, x=-\frac{10i\sqrt2}{2}

x=5i\sqrt 2, x=-5i\sqrt 2

x-5i\sqrt 2=0  and x+5i\sqrt 2=0

Hence, the factor of x^2+50 is given by

(x+5i\sqrt 2)(x-5i\sqrt 2)

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