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What else can I help you with?
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.
How many roots can a quadratic function have in total?
A quadratic function can have up to two roots. Depending on the discriminant (the expression under the square root in the quadratic formula), it can have two distinct real roots, one repeated real root, or no real roots at all (in which case the roots are complex). Therefore, the total number of roots, considering both real and complex, is always two.
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.
How many roots does the quadratic function have?
A quadratic function can have either two, one, or no real roots, depending on its discriminant (the expression (b^2 - 4ac) from the standard form (ax^2 + bx + c)). If the discriminant is positive, there are two distinct real roots; if it is zero, there is exactly one real root (a repeated root); and if it is negative, there are no real roots, only complex 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.
What does the solution represent in quadratic equations?
In quadratic equations, the solutions represent the values of the variable that make the equation true, typically where the graph of the quadratic function intersects the x-axis. These solutions can be real or complex numbers, depending on the discriminant (the part of the quadratic formula under the square root). Real solutions indicate points where the function crosses the x-axis, while complex solutions indicate that the graph does not intersect the x-axis. Overall, the solutions provide insight into the behavior and characteristics of the quadratic function.
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.
The graph of a quadratic function has it's turning point on the x-axis. How many roots does the function have?
If the turning point of a quadratic function is on the x-axis, it means the vertex of the parabola touches the x-axis, indicating that the function has exactly one root. This occurs when the discriminant of the quadratic equation is zero, resulting in a double root at the turning point. Therefore, the function has one real root.
What are the examples of a nature of the zeros of as quadratic function?
The nature of the zeros of a quadratic function, represented as ( ax^2 + bx + c = 0 ), can be determined using the discriminant ( D = b^2 - 4ac ). If ( D > 0 ), there are two distinct real zeros; if ( D = 0 ), there is one real zero (a double root); and if ( D < 0 ), there are no real zeros, but two complex zeros. These characteristics help in understanding the graph of the quadratic function and its intersections with the x-axis.
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
