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Can you have a quadratic function with one real root and one complex root?
Wiki User
∙ 14y ago
No you can not. Complex roots appear as conjugates. if a root is complex so is its conjugate. so either the roots are real or are both coplex.
Wiki User
∙ 14y ago
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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.
How many solutions does a quadratic equation have when it is expressed in the form of ax2 plus bx plus c0 where a does not 0?
Assuming a, b, and c are real numbers, there are three possibilities for the solutions, depending on whether the discriminant - the square root part in the quadratic formula - is positive, zero, or negative:Two real solutionsOne ("double") real solutionTwo complex solutions
Can there be a real and imaginary solution to a quadratic equation?
Yes, there can be a pure imaginary imaginary solution, as i2 =-1 and -i2 = 1. Or there can be a pure real solution or there can be a complex solution.For a quadratic equation ax2+ bx + c = 0, it depends on the value of the discriminant [b2 - 4ac], which is the value inside the radical of the quadratic formula.[b2 - 4ac] > 0 : Two distinct real solutions.[b2 - 4ac] = 0 : Two equal real solutions (double root).[b2 - 4ac] < 0 : Two complex solutions; they will be pure imaginary if b = 0, they will have both real and imaginary parts if b is nonzero.
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..
What is the method which is NOT a procedure in finding the roots of quadratic function?
Dividing by the square root of minus 1 and multiplying by the mass of a mature Adele penguin travelling at 'c' would not be a method for finding the roots of quadratic functions.
Can you have quadratic function with one real root and are complex root?
Yes, but in this case, the coefficients of the polynomial can not all be real.
What is Nature of the zeros of a quadratic function?
If you have a quadratic function with real coefficients then it can have: two distinct real roots, or a real double root (two coincidental roots), or no real roots. In the last case, it has two complex roots which are conjugates of one another.
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?
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.
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.
What does it mean when the graph of a quadratic function crosses the x axis twice?
When the graph of a quadratic crosses the x-axis twice it means that the quadratic has two real roots. If the graph touches the x-axis at one point the quadratic has 1 repeated root. If the graph does not touch nor cross the x-axis, then the quadratic has no real roots, but it does have 2 complex roots.
What are comparisons between a cubic and quadratic function?
They are both polynomial functions. A quadratic is of order 2 while a cubic is of order 3. A cubic MUST have a real root, a quadratic need not.
Is the inverse of a quadratic function is square root function?
yes
Does a quadratic function have to have 2 x-values?
If you mean have 2 different real x-value solutions then no.Otherwise a quadratic function will always have 2 solutions, just that they may both be the same value (repeated root) making it seem like there is only one solution value, or non-real (complex) making it seem like it has no solution value.
How do you find the range of a radical function?
The answer depends on what group or field the function is defined on. In the complex plane, the range is the complex plane. If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane. If the domain is non-negative real numbers, the range is also the real numbers.
What is the nature of zeros in quadratic function?
Nature Of The Zeros Of A Quadratic Function The quantity b2_4ac that appears under the radical sign in the quadratic formula is called the discriminant.It is also named because it discriminates between quadratic functions that have real zeros and those that do not have.Evaluating the discriminant will determine whether the quadratic function has real zeros or not. The zeros of the quadratic function f(x)=ax2+bx+c can be expressed in the form S1= -b+square root of D over 2a and S2= -b-square root of D over 2a, where D=b24ac.... hope it helps... :p sorry for the square root! i know it looks like a table or something...
Why is the most famous quadratic equation famous?
The quadratic formula is famous mainly because it allows you to find the root of any quadratic polynomial, whether the roots are real or complex. The quadratic formula has widespread applications in different fields of math, as well as physics.
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.
