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It is not always better.

Although quadratic equations always have solutions in the complex system, complex solutions might not always make any sense. In such circumstances, sticking to the real number system makes more sense that trying to evaluate an impossible solution in the complex field.

Q: Why is it better to solve quadratic equations in the complex number system rather than in the real number system?

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If the discriminant - the part under the radical sign in the quadratic formula - is negative, then the result is complex, it is as simple as that. You can't convert a complex number to a real number. If a particular problem requires only real-number solutions, then - if the formula gives complex numbers - you can state that there is no solution.

There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.

the first number out in front you pig

In algebra polynomials are the equations which can have any number of higher power. Quadratic equations are a type of Polynomials having 2 as the highest power.

The Julia can be generated by a quadratic equation in the complex plane. Select a complex number c. Then for a point z in the plane, carry out the iteration, zn+1 = zn2 + c. Colour-code the point according to how many iterations are required before its magnitude exceeds any given threshold. Repeat for all z in the region of the plane.

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If the discriminant - the part under the radical sign in the quadratic formula - is negative, then the result is complex, it is as simple as that. You can't convert a complex number to a real number. If a particular problem requires only real-number solutions, then - if the formula gives complex numbers - you can state that there is no solution.

There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.

the first number out in front you pig

In algebra polynomials are the equations which can have any number of higher power. Quadratic equations are a type of Polynomials having 2 as the highest power.

The Julia can be generated by a quadratic equation in the complex plane. Select a complex number c. Then for a point z in the plane, carry out the iteration, zn+1 = zn2 + c. Colour-code the point according to how many iterations are required before its magnitude exceeds any given threshold. Repeat for all z in the region of the plane.

Because of how close the two are. The only difference between the two is that a complex number is any whole number along side of a fraction, while a real number is any positive number.

Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.

Yes, if you have an equation az^2 + bz + c = 0 where a, b, and c are complex numbers, you can use the quadratic formula to find the (usually two) possible complex values for z. However, they will usually not be conjugates of each other.

The equation is -x2 - 4 = 14 or -x2 = 18 which is the same as x2 = -18. That is the quadratic equation.

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It is not to solve so much as to see the number of solutions and whether there is a real solution to the equation. b2 - 4(a)(c) A positive answer = two real solutions. A negative answer = no real solution ( complex solution i ) If zero as the answer there is one real solution.

You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.