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Q: How many solutions are possible for a system of equations containing exactly one linear and one quadratic equation?

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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.

No because quadratic equations only have 2 X-Intercepts

A quadratic equation ax2 + bx + c = 0 has the solutions x = [-b +/- sqrt(b2 - 4*a*c)]/(2*a)

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

radical equations have sq roots, cube roots etc. Quadratic equations have x2.

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If the discriminant of b2-4ac of the quadratic equation is greater the 0 then it will have 2 solutions.

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.

No because quadratic equations only have 2 X-Intercepts

A quadratic equation ax2 + bx + c = 0 has the solutions x = [-b +/- sqrt(b2 - 4*a*c)]/(2*a)

There is no quadratic equation that is 'linear'. There are linear equations and quadratic equations. Linear equations are equations in which the degree of the variable is 1, and quadratic equations are those equations in which the degree of the variable is 2.

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

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.

If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.

The answer depends on the nature of the equation. Just as there are different ways of solving a linear equation with a real solution and a quadratic equation with real solutions, and other kinds of equations, there are different methods for solving different kinds of imaginary equations.

Pros: There are many real life situations in which the relationship between two variables is quadratic rather than linear. So to solve these situations quadratic equations are necessary. There is a simple equation to solve any quadratic equation. Cons: Pupils who are still studying basic mathematics will not be told how to solve quadratic equations in some circumstances - when the solutions lie in the Complex field.

radical equations have sq roots, cube roots etc. Quadratic equations have x2.

If the discriminant of the quadratic equation is greater than zero then it will have two different solutions. If the discriminant is equal to zero then it will have two equal solutions. If the discriminant is less than zero then it will have no real solutions.