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Q: Do quadratic equations always have two real solutions?

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There are many ways quadratic equations are used in the real world. These equations are used to calculate area, speed and profit

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.

December 3rd, 2029!

Suppose the quadratic equation is ax^2 + bx + c = 0 and D = b^2 - 4ac is the discriminant. Then the solutions to the quadratic equation are [-b Â± sqrt(d)]/(2a). Since D = 0, the both solutions are equal to -b/(2a), a single real solution.

The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.

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

It is not always better.Although quadratic equations always have solutions in the complex system, complex solutions might not always make any sense. In such circumstances, sticking to the real number system makes more sense that trying to evaluate an impossible solution in the complex field.

The quadratic has no real solutions.

A quadratic equation can have either two real solutions or no real solutions.

There are many ways quadratic equations are used in the real world. These equations are used to calculate area, speed and profit

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.

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.

In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.

It will then have two equal real solutions

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

You will apply them when solving quadratic equations in which the quadratic expression cannot be factorised.

December 3rd, 2029!

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