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Is it possible for a quadratic equation to have no real solution? please give an example and explain. Thank you

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16y ago

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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.


Explain how you an determine if the number is a solution of an equation?

Substitute the number in the equation. If the resulting statement is true the number is a solution to the equation.


How do you explain algebra?

Algebra is the usage of variables (e.g. x,y) in order to make the solution of an equation have many possible answers.


Explain how to identify whether an equation has no solution or infinitely many solutions?

An equation can be determine to have no solution or infinitely many solutions by using the square rule.


Explain how to solve a quadratic equation explain how to determine and find the different types of solutions. describe at least two differents methods ( graphing factoring or quadratic formula?

To solve a quadratic equation, you can use methods like factoring, graphing, or the quadratic formula. Factoring involves rewriting the equation as a product of binomials, allowing you to set each factor to zero and solve for the variable. Graphing involves plotting the quadratic function and identifying the x-intercepts, which represent the solutions. The quadratic formula, ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), provides the solutions directly from the coefficients of the equation ( ax^2 + bx + c = 0 ), where the discriminant ( b^2 - 4ac ) indicates the nature of the solutions: two real and distinct, one real and repeated, or two complex.


How do you write a word problem involving a quadratic function. How would you explain the steps in finding the solution?

To write a word problem involving a quadratic function, start by identifying a real-world scenario that can be modeled by a quadratic relationship, such as projectile motion or area optimization. Frame the problem by describing the situation, including key variables and relationships, and use specific numbers to make it concrete. To find the solution, set up the quadratic equation based on the problem context, apply techniques like factoring, completing the square, or using the quadratic formula, and interpret the results in the context of the original scenario. Finally, check if the solutions make sense within the problem’s constraints.


Which statement best explain why there is no real solution to the quadratic equation 2x2 plus x plus 7 equals 0?

The discriminant says; b^2 - 4ac 1^2 - 4(2)(7) = 1 - 56 < 1 So, less than 1 and no real roots


Explain a Quadratic equation and how to solve it?

A quadratic equation is any equation that can be expressed as ax2 + bx + c = 0.Note that the a, b and c are specified, x is the only unknown.Example:x2 - 10x - 24 = 0a, b, c are the coefficients of each term.Now x2 appears not to have a coefficient, but remember x2 is the same thing as 1x2 so the coefficient is 1. So a = 1.The second term has a coefficient of -10 because it has a minus, not plus sign in front of it so b = -10.Likewise for c, the third term. C = -24.So you have your terms.There are two popular ways of solving this.You can factorise the equation, or use the Quadratic Formula.I prefer to use the Quadratic Formula, as it is very straightforward, you just need to practise it.The quadratic formula is x = (-b±√(b2-4ac))/2a


Explain why the roots of a quadratic equation are imaginary if the value of the discriminant is less than 0?

The square of any real number is non-negative. So no real number can have a negative square. Consequently, a negative number cannot have a real square root. If the discriminant is less than zero, the quadratic equation requires the square root of that negative value, which cannot be real and so must be imaginary.


How do you explain the steps of a fraction equation by adding?

First find a common denominator. Then, add the numerators together. Simplify if possible.


How many existing methods are there in solving quadratic equations?

There are 5 existing methods in solving quadratic equations. For the first 4 methods (quadratic formula, factoring, graphing, completing the square) you can easily find them in algebra books. I would like to explain here the new one, the Diagonal Sum Method, recently presented in book titled:"New methods for solving quadratic equations and inequalities" (Trafford 2009). It directly gives the 2 roots in the form of 2 fractions, without having to factor the equation. The innovative concept of the method is finding 2 fractions knowing their Sum (-b/a) and their Product (c/a). It is very fast, convenient and is applicable whenever the given quadratic equation is factorable. In general, it is hard to tell in advance if a given quadratic equation can be factored. However, if this new method fails to find the answer, then we can conclude that the equation can not be factored, and consequently, the quadratic formula must be used. This new method can replace the trial-and-error factoring method since it is faster, more convenient, with fewer permutations and fewer trials.


Explain the concept of correlation and regression line as a forecasting tool?

once an equation for a regression is derived it can be used to predict possible future