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A quadratic equation ax2 + bx + c = 0 has the solutions
x = [-b +/- sqrt(b2 - 4*a*c)]/(2*a)
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What is the solution of rational equations reducible to quadratic?
They are the solutions for the reduced quadratic.
When the discriminant is perfect square the answer to a quadratic equation will be?
Rational.
Does there exist a quadratic equation whose coefficients are irrational but both the roots are rational?
None, if the coefficients of the quadratic are in their lowest form.
Do all rational equations have a single solution?
Not all rational equations have a single solution but can have more than one because of having polynomials. All rational equations do have solutions that cannot fulfill the answer.
Why do you check your answers for rational equations and radical equations?
You plug the number back into the original equation. If you have a specific example, that would help.
What is the solution of rational equations reducible to quadratic?
They are the solutions for the reduced quadratic.
When the discriminant is perfect square the answer to a quadratic equation will be?
Rational.
What is the difference with equations with integers and equations with rational numbers?
It is a trivial difference. If you multiply every term in the equation with rational numbers by the common multiple of all the rational numbers then you will have an equation with integers.
Is there a difference between rational expressions and rational equations?
Yes. An equation has an "=" sign.
Does there exist a quadratic equation whose coefficients are irrational but both the roots are rational?
None, if the coefficients of the quadratic are in their lowest form.
Do all rational equations have a single solution?
Not all rational equations have a single solution but can have more than one because of having polynomials. All rational equations do have solutions that cannot fulfill the answer.
Why do you check your answers for rational equations and radical equations?
You plug the number back into the original equation. If you have a specific example, that would help.
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.
How can you determine whether a polynomial equation has imaginary solutions?
To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.
What statement must be true of an equation before you can use the quadratic formula to find the solutions?
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.
Why is factoring a valuable tool for solving quadratic equations?
In some simple cases, factoring allows you to find solutions to a quadratic equations easily.Factoring works best when the solutions are integers or simple rational numbers. Factoring is useless if the solutions are irrational or complex numbers. With rational numbers which are relatively complicated (large numerators and denominators) factoring may not offer much of an advantage.
What is equivalent ratio's equation?
Equations are said to be equivalent if they have the same solution. This definition also holds true in rational equations or equations involving rational expressions. For instance, the equations 2x = 14 and x - 3 = 4 are equivalent. Why? It's because they have the same solution, that is x = 7.
