The <em>cubic</em> equation f(x) = x³ + 2 · x² + 4 · x + 8 has one <em>real</em> root and two <em>complex</em> roots.
<h3>What kind of roots does have a cubic equation? </h3>
In this problem we have a <em>cubic</em> equation and the nature of their roots must be inferred according to a <em>algebraic</em> method.
Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an <em>analytical</em> method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.
The discriminant is described below:
Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² (1)
Where:
- There are three <em>distinct real</em> roots for Δ > 0.
- Real roots with multiplicity greater than 1 for Δ = 0.
- A <em>real</em> root and two <em>complex</em> roots for Δ < 0.
If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:
Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²
Δ = - 1024
The <em>cubic</em> equation f(x) = x³ + 2 · x² + 4 · x + 8 has one <em>real</em> root and two <em>complex</em> roots.
To learn more on <em>cubic</em> equations: brainly.com/question/13730904
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Answer:
Step-by-step explanation:
A square surface is determined by the product of its sides
s = L ^ 2
Thus, the surface of the cardboard of side C, will be
x ^ 2 + 12x + 36 = C ^ 2
Factoring
(x + 6) (x + 6) = C ^ 2
THE SIDE IS (x + 6)
Answer:
My answer got deleted so I gotta answer this again...
Step-by-step explanation:
4+3x+(-8)+4x
The sum of means to add so the sum of 4 = 4+
three times a number = 3×x or simply 3x
+(-8)
four times a number = 4×x or simply 4x
Combine the terms into an addition problem and you get
4+3x+(-8)+4x
A circle is 360 degrees. 360-90 is 270. That is the answer: 270
