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Put the equation in the form ax2 + bx + c = 0. Replace a, b, and c in the quadratic formula: x = (-b (plus-or-minus) root(b2 - 4ac)) / 2a. Look at the term under the radical sign, which I wrote as "root" here. If b2 - 4ac is...
- Positive: the equation has two real solutions.
- Zero: the equation has one ("double") solution.
- Negative: the equation has two complex solutions (and therefore no real solution).
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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.
What does coefficients of a quadratic equation mean?
A coefficient is the number before the variable (e.g. the 3 in 3x, or the 22 in 22x^2). For example, in the following quadratic equation, the coefficient to x is 4, and the coefficient to y is 12. 4x^2+12y+4 Remember that a number preceded by a ^ is a power, i.e 4x^2 is 4x squared.
Can you solve a quadratic equation by completing the square even though it is not a perfect square?
Yes, it won't be exact, but you can round the number to get a close estimate.
How many sides does a polygon have if it has 902 diagonals?
Let n be the number of sides: 1/2*(n2-3n) = diagonals 1/2*(n2-3n) = 902 Multiply both sides by 2 and form a quadratic equation: n2-3n-1804 = 0 Solving the above by means of the quadratic equation formula gives a positive value for n as 44 Therefore the polygon has 44 sides
A polygon has 14 diagonals how many sides does it have?
To determine the number of sides in a polygon with 14 diagonals, we can use the formula for the number of diagonals in a polygon: D = n(n-3)/2, where n is the number of sides. By setting D = 14 and solving for n, we get n(n-3)/2 = 14. Simplifying this equation, we find that n^2 - 3n - 28 = 0. Factoring this quadratic equation, we get (n-7)(n+4) = 0. Therefore, the polygon has either 7 or -4 sides. Since the number of sides cannot be negative, the polygon must have 7 sides.
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.
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 discriminant to determine how many real number solutions the quadratic equation -4j2 plus 3j-28 equals 0 has?
The discriminant is -439 and so there are no real solutions.
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.
How many solutions does the equation have?
The number of solutions an equation has depends on the nature of the equation. A linear equation typically has one solution, a quadratic equation can have two solutions, and a cubic equation can have three solutions. However, equations can also have no solution or an infinite number of solutions depending on the specific values and relationships within the equation. It is important to analyze the equation and its characteristics to determine the number of solutions accurately.
Use the discriminant to determine how many real number solutions the quadratic equation -4j to the second power plus 3j - 28 equals 0 has?
It has no real roots.
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 quadratic equation of x2 equals -11 using the complex number system?
13
Can a graph be used to determine the number of solutions an equation has?
Yes.
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.
How do you determine the number of solutions of an equation?
the maximum number of solutions to an euation is equal to the highest power expressed in the equation. 2x^2=whatever will have 2 answers
What is true of the discriminant when the two real number solutions to a quadratic equation are rational numbers?
The discriminant must be a perfect square or a square of a rational number.
