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Could you have a quadratic function with one real root and one complex root Think about what the graph of that function might look like. What might the function itself look like?
Wiki User
∙ 7y ago
Yes; to have a quadratic function with two given roots, just decide what roots you want to have - call them "a" and "b" - and write your function as:y = (x - a) (x - b)
You can multiply this out if you wish, to make it look like a standard quadratic function. Note that "a" and "b" can be any complex numbers.
Graphing such a function is quite complicated; to graph both the x-value and the y-value, each of which is itself a complex (i.e., two-dimensional) number, you really need four dimensions.
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoYes it could. If the real root was r and the complex root was c, then x^2 - (r + c)*x + r*c would have one real and one complex root. Of course, the coefficients of x and the constant term would not be real but if you are in the complex domain then there is no reason to restrict your coefficients to real numbers.
Wiki User
∙ 7y agoIf the quadratic function has complex terms in it, then you could have one real and one complex root. For example, (x-2)(x-3i-4)=0 has roots of 2 and 3i+4.
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Could there be a quadratic function that has an undefined axis of symmetry?
Yes and this will happen when the discriminant of a quadratic equation is less than zero meaning it has no real roots.
Could you have a quadratic function with one real root and one complex root?
Provided some of the coefficients and the constant were imaginary (complex) as well, yes. For example, (x + 2)(x - 3+i) has both a real and an imaginary root, and has coefficients that are also both real and imaginary, i.e. 1, -1+i, and -6+2i.
Could you have a quadratic function with one real root and one complex root What might the function itself look like?
Short answer: No.Assuming that the original quadratic is completely real, complex roots always come in conjugate pairs - meaning that if you multiplied both of the complex roots together, you would get a real number. For example, if one root was 2 + 3i, then you know that another root will be 2 - 3i, because those two multiplied together give you -5 (thanks to (x2 - y2) = (x+y)(x-y). You see how math all fits together? It's great!)Therefore, a real quadratic can only have 2 real roots or 2 complex roots. If you have one of each, either something has gone horribly wrong or your teacher is a sadist.Also, bear in mind that I've only done A level (American translation: late high school/early college) math, so this might be wrong if you're past that level.
Is it possible to have different quadratic equations with the same solution Why?
Yes it is possible. The solutions for a quadratic equation are the points where the function's graph touch the x-axis. There could be 2 places to that even if the graph looks different.
Are quadratic functions symmetric with respect to the y-axis?
No, but they are symmetric with respect to a line parallel to the y-axis - which could be the y-axis itself.
How do you compute the intercepts of a quadratic function?
Use the quadratic equation. If ax+bx+c=0 x=(-b±(b^2-4ac)^(1/2))/2a. You could also complete the square, factor,or graph the equation.
What do IPCs function as?
Intelligent project coaches (IPCs) could function as coworkers, assisting and collaborating with design or operations teams for complex systems.
How can a function return multiple values in plsql?
You cannot return multiple values from a function. A function returns one or no values. That is the definition of a function. That said, you could have that one value be a pointer to a struct, or it could be a struct itself, and that struct could contain multiple values. You can also pass the function pointers to items in the caller's address space that the function could modify.
Installing a ford exploer engine?
This is much too complex for WikiAnswers. It could take an entire website by itself.
How many complex number solutions can exist for a quadratic equation?
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.
Can the roots of a quadratic be listed as ordered pairs?
In the case of real roots, you could, but the second part of the ordered pair (the ordinate) will always be zero, so there is not much point.In the case of complex roots (or real roots in the complex field), you could list them as ordered pairs: with (a, b) representing a + bi where i is the imaginary square root of -1..
Could you ever have three solutions to a quadratic equation?
No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).
