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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.
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What is the quadratic equation of x2 equals -11 using the complex number system?
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What is the difference between quadratic formula and quadratic equation?
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
What happens when there is negative under the square root in a quadratic equation?
When there is a negative number under the square root in a quadratic equation, it indicates that the equation has no real solutions. Instead, it results in complex or imaginary solutions, as the square root of a negative number involves the imaginary unit (i). This situation occurs when the discriminant (the part under the square root in the quadratic formula) is negative. Consequently, the quadratic graph does not intersect the x-axis, indicating no real roots.
Why does a quadratic formula have two solutions?
A quadratic equation, typically in the form ( ax^2 + bx + c = 0 ), is a polynomial of degree two, which means its graph is a parabola. According to the Fundamental Theorem of Algebra, a polynomial of degree ( n ) has exactly ( n ) roots (solutions) in the complex number system. Therefore, a quadratic equation has two solutions, which can be real or complex, depending on the discriminant (( b^2 - 4ac )). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution (a double root); and if it is negative, there are two complex solutions.
How do you find the number of solutions in a quadratic equation?
Factoring by the AC method, difference of squares, perfect square trinomial. If not factorable by those ways, you can use the quadratic formula. You can also find zeros by synthetic division. If there are not any real solutions, then the solutions are said to be complex, they do not cross the x axis.
What is the quadratic equation of x2 equals -11 using the complex number system?
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How many solution will there be if the quadratic equation does not touch or cross the x-axis?
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
In general how many distinct solutions are there to a quadratic equation?
the maximum number of solutions to a quadratic equation is 2. However, usually there is only 1.
What is the difference between quadratic formula and quadratic equation?
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
Why does a quadratic formula have two solutions?
A quadratic equation, typically in the form ( ax^2 + bx + c = 0 ), is a polynomial of degree two, which means its graph is a parabola. According to the Fundamental Theorem of Algebra, a polynomial of degree ( n ) has exactly ( n ) roots (solutions) in the complex number system. Therefore, a quadratic equation has two solutions, which can be real or complex, depending on the discriminant (( b^2 - 4ac )). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution (a double root); and if it is negative, there are two complex solutions.
Why does the discriminant determine the number and type of the solutions for a quadratic equation?
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
How do you find the number of solutions in a quadratic equation?
Factoring by the AC method, difference of squares, perfect square trinomial. If not factorable by those ways, you can use the quadratic formula. You can also find zeros by synthetic division. If there are not any real solutions, then the solutions are said to be complex, they do not cross the x axis.
Explain how the number of solutions for a quadratic equation relates to the graph of the function?
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
What does it mean if the value under the radical sign in the quadratic formula is negative?
If the value under the radical sign (the discriminant) in the quadratic formula is negative, it means that the quadratic equation has no real solutions. Instead, it has two complex (or imaginary) solutions. This occurs because the square root of a negative number is not defined in the set of real numbers, indicating that the parabola represented by the equation does not intersect the x-axis.
What is the quadratic equation of -x2-4 equals 14 using the complex number system?
The equation is -x2 - 4 = 14 or -x2 = 18 which is the same as x2 = -18. That is the quadratic equation.
How do you find the answer to a quadratic equation from the quadratic formula?
Plug 'a', 'b', and 'c' from the equation into the formula. When you do that, the formula becomes a pair of numbers ... one number when you pick the 'plus' sign, and another number when you pick the 'minus' sign. Those two numbers are the 'solutions' to the quadratic equation you started with.
What is the number called under the square root when the number is negative in the quadratic equation?
The term inside the square root symbol is called the radicand. There isn't a specific term for it based on its sign; whether it's positive or negative, it's still the radicand.I'm a little confused by your reference to the quadratic equation.If the radicand is negative, the root is an imaginary number, though that doesn't specifically have anything to do with the quadratic equation in particular.If the quantity b2 - 4ac is negative in the quadratic equation, the root of the quadratic equation is either complex or imaginary depending on whether or not b is zero.---------------------------Thank you to whoever answered this first; you saved me a bit of trouble explaining this to the asker :)However, in the quadractic equation, the number under the radical is called the discriminant. This determines the number of solutions of the quadratic. If the radicand is negative, this means that there are no real solutions to the equation.
