Yes, but in this case, the coefficients of the polynomial can not all be real.
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.
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.
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.
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.
yes
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.
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.
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.
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.
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.
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.
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.
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.
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.
yes
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.
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.