Using the quadratic formula, we solve for
.

Taking square roots on both sides, we end up with

Compute the square roots of -171 + 140i.


By de Moivre's theorem,

and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find

as well as the fact that


(whose signs are positive because of the domain of
).
This leaves us with

Compute the square roots of 5 + 12i.


By de Moivre,

and its negative, -3 - 2i. We use similar reasoning as before:




Lastly, compute the roots of -2i.



as well as -1 + i.
So our simplified solutions to the quartic are

<span>fourth degree polynomial with three terms
the degree is the highest exponent the term are separated by plus or minus </span>
Answer:
82 inches
Step-by-step explanation:
The difference between consecutive even integers is 2, thus
let the legs be n and n + 2
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
n² + (n + 2)² = 58² ← expand and simplify left side
n² + n² + 4n + 4 = 3364 ( subtract 3364 from both sides )
2n² + 4n - 3360 = 0 ( divide all terms by 2 )
n² + 2n - 1680 = 0 ← in standard form
(n + 42)(n - 40) = 0 ← in factored form
Equate each factor to zero and solve for n
n + 42 = 0 ⇒ n = - 42
n - 40 = 0 ⇒ n = 40
But n > 0 ⇒ n = 40
and n + 2 = 40 + 2 = 42
Thus sum of legs = 40 + 42 = 82 inches
Answer:
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