Questions on Algebra: Complex Numbers answered by real tutors!

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x^-2 - 15x^-1 + 44 = 0

Multiply by x^2
1 - 15x + 44x^2 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation ax^2+bx+c=0

(in our case 44x^2+-15x+1 = 0

) has the following solutons:

$x[12] = (b+-sqrt( b^2-4ac ))/2\a$

For these solutions to exist, the discriminant b^2-4ac

should not be a negative number.

First, we need to compute the discriminant b^2-4ac

.

Discriminant d=49 is greater than zero. That means that there are two solutions: $x[12] = (--15+-sqrt( 49 ))/2\a$ .

$x[1] = (-(-15)+sqrt( 49 ))/2\44 = 0.25$
$x[2] = (-(-15)-sqrt( 49 ))/2\44 = 0.0909090909090909$

Quadratic expression 44x^2+-15x+1

can be factored:
44x^2+-15x+1 = (x-0.25)*(x-0.0909090909090909)

Again, the answer is: 0.25, 0.0909090909090909. Here's your graph:
graph( 500, 500, -10, 10, -20, 20, 44*x^2+-15*x+1 )

x = 0.25, x=1/11