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Yes and sometimes the two solutions are equal

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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: Do you agree that quadratic equations has at most two solutions?
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Related questions

Most quadratic equations have?

two solutions

Most quadratic equations have what?

Two solutions

Most quadratic equations have how many solutions?


Most quadric equations have?

A quadratic equation can have two real solutions, one real solution, or two complex solutions, none of them real.

Why are there usually two solutions to a quadratic equation?

In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.

Could you ever have three solutions to a quadratic equation?

No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).

What is a system of linear equations in two variables?

They are a set of equations in two unknowns such that any term containing can contain at most one of the unknowns to the power 1. A system of linear equations can have no solutions, one solution or an infinite number of solutions.

How do you find solutions to quadratic eqations?

There are several ways to solve such equations: (1) Write the equation in the form polynomial = 0, and solve the left part (where I wrote "polynomial"). (2) Completing the square. (3) Use the quadratic formula. Method (3) is by far the most flexible, but in special cases methods (1) and (2) are faster to solve.

Why are there usually two solutions in quadratic equations?

It is easier to understand this if you draw the curve of the equation as a graph. From the graph you will see that the line curves back on itself, usually in a nice parabolic curve. Because it curves back, you find that most values of Y correspond to two different values of X - so there are two solutions.

What is the most challenging mathematics question in junior secondary?

How about that when given a quadratic equation what would you use to determine whether or not it has any solutions.

Can all quadratic equations be solved?

Well, that depends on what you mean "solve by factoring." For any quadratic equation, it is possible to factor the quadratic, and then the roots can be recovered from the factors. So in the very weak sense that every quadratic can be solved by a method that involves getting the factors and recovering the roots from them, all quadratic equations can be solved by factoring. However, in most cases, the only way of factoring the quadratic in the first place is to first find out what its roots are, and then use the roots to factor the quadratic (any quadratic polynomial can be factored as k(x - r)(x - s), where k is the leading coefficient of the polynomial and r and s are its two roots), in which case trying to recover the roots from the factors is redundant (since you had to know what the roots were to get the factors in the first place). So to really count as solving by factoring, it makes sense to require that the solution method obtains the factors by means that _don't_ require already knowing the roots of the polynomial. And in this sense, most quadratic equations are not solvable through factoring.

What would happen if you went through a wormhole?

Wormholes are not proven to exist. There are mathematical theories that they may, however there are several different solutions to the equations. The most likely is that you would simply disappear, effectively you would die. There are low probability solutions that you may emerge elsewhere or elsewhen but these solutions are by no means clear.

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