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embizze | High School Teacher | (Level 2) Educator Emeritus

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`x^2+13` is an expression.

(1) If you are asked to solve `x^2+13=0 ` :

`x^2+13=0 `

`x^2=-13 `  There will be no real solutions but:

`x=+-sqrt(-13) `

`x=+-isqrt(13) ` where `i ` is the imaginary unit and `i=sqrt(-1) `

Alternatively you can either complete the square or use the quadratic formula:

`x=(0+-sqrt(0-4(1)(13)))/2 ==> x=+-sqrt(-13) ` as above.

(2) If you are asked to factor the expression, note that the sum of squares does not factor in the real numbers. By the fundamental theorem of algebra, it will factor in the complex numbers:

`x^2+13=(x+isqrt(13))(x-isqrt(13)) `

(3) Note that the discriminant `o^2-4(1)(13)<0 ` so there are 2 complex roots.

(4) The graph of `y=x^2+13 ` is a parabola opening up with vertex at (0,13):




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