Write a quadratic equation that has two imaginary solutions

It is sometimes claimed that his equations for planetary motions anticipated the Laws of Motion discovered by Kepler and Newton, but this claim is doubtful. Perhaps the most elementary angle system is degrees, which breaks a circle into equal parts.

Several theorems bear his name, including the formula for the area of a cyclic quadrilateral: Although he himself attributed the theorem to Archimedes, Al-Biruni provided several novel proofs for, and useful corollaries of, this famous geometric gem.

This is to obtain an x2 term with a coefficient of 1. We will discuss projectile motion using parametric equations here in the Parametric Equations section.


Eudoxus was the first great mathematical astronomer; he developed the complicated ancient theory of planetary orbits; and may have invented the astrolabe. His theories of physics would seem quaint today, but he seems to have been the first to describe magnetism and static electricity.

In this example 6 and -1 are called the elements of the set. Later, Tartaglia was persuaded by Gerolamo Cardano — to reveal his secret for solving cubic equations. We therefore use the theorem from the previous section.

While Al-Biruni may lack the influence and mathematical brilliance to qualify for the Tophe deserves recognition as one of the greatest applied mathematicians before the modern era. He preserved some of the teachings of Aryabhata which would otherwise have been lost; these include a famous formula giving an excellent approximation to the sin function, as well as, probably, the zero symbol itself.

Although this work might be considered the very first study of linguistics or grammar, it used a non-obvious elegance that would not be equaled in the West until the 20th century.

He wrote the book Al-Jabr, which demonstrated simple algebra and geometry, and several other influential books.

Quadratic Equations with Imaginary Solutions

He improved on the Ptolemaic model of planetary orbits, and even wrote about though rejecting the possibility of heliocentrism. Quadratic Application Problem A ball is thrown in the path, measured in feet: He was also noted for his poetry.

Among the several great and famous Baghdad geometers, Thabit may have had the greatest genius. Many of his works have been lost, including proofs for lemmas cited in the surviving work, some of which are so difficult it would almost stagger the imagination to believe Diophantus really had proofs.

The words philosophy and mathematics are said to have been coined by Pythagoras. There is information on the parametric form of the equation of a line in space here in the Vectors section. Welcome to She Loves Math! Construction of the regular heptagon is another such task, with solutions published by four of the men on this List: Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.

His science was a standard curriculum for almost years. Persia used the base Babylonian system; Mayans used base To get to the bottom of this mystery, we must return to first principles by considering the nature of circles, and especially the nature of angles.

Notice that if the c term is missing, you can always factor x from the other terms.

Why quadratic equation may have complex solutions?

Welcome to She Loves Math! We now have Step 5 Take the square root of each side of the equation. The Greeks borrowed from Babylonian mathematics, which was the most advanced of any before the Greeks; but there is no ancient Babylonian mathematician whose name is known. Babylon was much more advanced than Egypt at arithmetic and algebra; this was probably due, at least in part, to their place-value system.

He is often credited with inventing the names for parabola, hyperbola and ellipse; but these shapes were previously described by Menaechmus, and their names may also predate Apollonius. OK, use your imaginations on this one sorry! One Real Root If the discriminant of a quadratic function is equal to zero, that function has exactly one real root and crosses the x-axis at a single point.

And remember that this is just one way to write the set of parametric equations; there are many! We can do this by completing the square as, Solving for x and simplifying we have, Thus, the roots of a quadratic function are given by, This formula is called the quadratic formula, and its derivation is included so that you can see where it comes from.

His work was cited by Ptolemy, Pappus, and Thabit; especially the Theorem of Menelaus itself which is a fundamental and difficult theorem very useful in projective geometry. The circle functions are coordinates on the unit circle. Another version has Hippasus banished for revealing the secret for constructing the sphere which circumscribes a dodecahedron.Solution to Problem 1: The given equation x 2 + 2x = -1 ; Write the above quadratic equation with right side equal to 0.

x 2 + 2x + 1 = 0 ; Factor the equation. (x + 1) 2 = 0 Solve the equation to obtain the repeated kitaharayukio-arioso.com (The graph of this quadratic polynomial will therefore be a parabola that never touches the x-axis.) The Discriminant As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b 2 - 4 ac), is positive, negative, or kitaharayukio-arioso.com  · shows that the function has two real roots, one equation.

3. Write the square root of both sides of the resulting equation and solve for x. A1 2bB 2 ax2 1 bx 2 c 5 0 Cpgs 8/12/08 PM Page Not every second-degree polynomial 4.

5.) 5) Quadratic kitaharayukio-arioso.com Version The DeleteLookupCol macro command will delete a specified column in an existing Lookup table.

The format of the command is DeleteLookupColumn 'TableName' 'ColumnName' where Tablename and ColumnName can be string constants or string variables.

· Best Answer: a discriminant is just what's under the radical in the quadratic formula. b^2 - 4ac if the discriminant is positive, there is a real answer, if it is negative, there is not. I'm not sure about the rules about one or two real kitaharayukio-arioso.com › Science & Mathematics › Mathematics.

How to Create a Simple Quadratic Formula Program on the TI-89 and Voyage 200

· QUADRATIC EQUATIONS. A quadratic equation is always written in the form of: 2. ax +bx +c =0 where. a ≠0. The form. ax. 2 When the discriminant is positive but not a perfect square, the equation has two irrational solutions.

Example: x2 +4x −6 =0. The discriminant. ← Write the squared number in binomial kitaharayukio-arioso.com://kitaharayukio-arioso.com

Write a quadratic equation that has two imaginary solutions
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