1 Answer

EscapeArtist · Answer 1 · 2021-04-19T17:37:26+0000

Answer:

$x=\frac{1+5i} {2}$ and
$x=\frac{1-5i} {2}$

Explanation:

we know that

The formula to solve a quadratic equation of the form

ax^(2) +bx+c=0

is equal to

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

in this problem we have

f(x)=2x^(2) -2x+13

Equate the function to zero

2x^(2) -2x+13=0

so

$a=2\\b=-2\\c=13$

substitute in the formula

$x=\frac{-(-2)\pm\sqrt{-2^(2)-4(2)(13)}} {2(2)}$

$x=\frac{2\pm√(-100)} {4}$

Remember that

i=√(-1)

so

$x=\frac{2\pm10i} {4}$

Simplify

$x=\frac{1\pm5i} {2}$

therefore

$x=\frac{1+5i} {2}$ and
$x=\frac{1-5i} {2}$

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