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1 answer:
The equation looks like this 
. In an ellipse, a is always the bigger value, so a^2 = 25. This bigger value also tells us which axis is the major one. Sine the bigger value a is under the y^2 of the equation, the major axis is the y-axis. This is a vertical ellipse. The center is always found within a set of parenthesis that exist with the x^2 and the y^2. Since there are no parenthesis with either, there is no side to side movement, nor is there any up or down movement. So the center doesn't move from the origin (0, 0). The vertex is also along the major axis, and if a^2 is 25, then a = 5, so the vertices go up 5 from the center and down 5 from the center. Vertices are (0, 5) and (0, -5). The foci follow the formula 
. c is the distance that the foci are from the center. 
and c = 3. The foci also lie on the major axis, so the coordinates for the foci are (0, 3) and (0, -3). There you go!
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Answer:
The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are .
Step-by-step explanation:
Consider the provided information.
Algebra's fundamental theorem states that: Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.
Now consider the provided equation.
The degree of the polynomial equation is 2, therefore according to Algebra's fundamental theorem the equation have two complex roots.
Now find the root of the equation.
For the quadratic equation of the form the solutions are:
Substitute in above formula.
Hence, the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are .