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Topic: **Quadratic equation homework****Question:**
I just have a quick question about quadratic equations, when do you know when to use the imaginary numbers? like in some answers on my homework there are answers with the i, and in others there are none, why is that? please help and thank you so much :D

July 23, 2019 / By Alisha

The general solution to a quadratic equation of the form ax² + bx + c = 0 is: x = [-b±√(b²-4ac)]/(2a) If the radicand, b²-4ac, also known as the discriminant, is less than zero, the solution involves the square root of a negative number which invokes √(-1) which is usually represented by "i". If the discriminant is greater than or equal to zero, then the square root does not involve a negative number and "i" is not part of the solution. So sometimes the solution includes "i" (b²-4ac < 0) and sometimes is does not (b²-4ac ≥ 0).

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Did you like the answer? We found more questions related to the topic: **Quadratic equation homework**

Graphing is probably the least useful of the methods for finding solutions, since it is so inaccurate. On the other hand, the graph is quite useful for understanding the general behavior of a quadratic function. The quadratic formula always works, and is my personal preference for solving quadratic equations for that reason. The only problem with it is that it can take longer than factoring in the case of an equation that happens to be easy to factor. However, the solutions you find using the quadratic formula may be used to factor a quadratic, so the formula is even more useful than you might think at first. Completing the square basically leads you to the same computations as using the quadratic formula, but involves extra algebra as well. It is mostly useful for deriving the quadratic formula, and for a few other similar derivations. Factoring is often the fastest technique when it works, but most quadratic equations cannot be factored, and it isn't all that easy to tell whether you can or cannot factor any particular equation.

use quadratic formula when the solution is not immediately obvious or the roots are not integers. Complete the square when you can't get the equation into the form where the roots can be read off. Factorizing can be done if the coefficient is large. and graphing can be done when your either bored :P or the relationship between the solutions must be made obvious.

My favorite method is using the formula. Graphing can get too complicated and factoring does not always work out evenly.

If there's a square root of a minus number required, it will have an imaginary pair of roots. So if we require rt (-36), it's rt(-1)rt(36) = 6i.

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6 a^2-18 a = 18 Divide both sides by 6: a^2-3 a = 3 Add 9/4 to both sides: a^2-3 a+9/4 = 21/4 Factor the left hand side: (a-3/2)^2 = 21/4 Take the square root of both sides: abs(a-3/2) = sqrt(21)/2 Eliminate the absolute value: a-3/2 = -sqrt(21)/2 or a-3/2 = sqrt(21)/2 Add 3/2 to both sides: a = 1/2 (3-sqrt(21)) or a-3/2 = sqrt(21)/2 Add 3/2 to both sides: a = 1/2 (3-sqrt(21)) or a = 1/2 (3+sqrt(21))

They have a common factor of 6, so divide everything by 6 first: 6(a² - 3a - 3) = 0 But if you copied that correctly, you'll need to use the quadratic formula or complete the square to solve this. Reverse FOIL won't work.

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