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A rational equation can be multiplied by the least common multiple of its denominators to make it into a polynomial equation. The degree of this polynomial is the highest power (of the variable) that appears in it.

It can be proven that a polynomial of degree n must have n roots in the complex domain. However, there may be fewer roots in the real domain. This is because if the coefficients are real then there may be pairs of complex roots [conjugates] which will not count as real roots. Also, there may be identical roots of multiple order. For example,

x4 - 1 = 0 has 4 complex roots. These are 1, -1, i and -i where i is the imaginary root of -1.

There are only 2 real roots -1 and +1.

x4 = 0 has 4 multiple roots, each of which is 0. Thus x = 0 is a root of multiplicity 4.

Q: How can a rational equation have more than one solution?

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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.

YES

Yes and sometimes it can have more than one solution.

True

yes, if it is in brackets and the equation is doubled. (These are the words of my grade 12 teacher)

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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.

YES

The solution set is the answers that make an equation true. So I would call it the solution.

Yes and sometimes it can have more than one solution.

True

yes, if it is in brackets and the equation is doubled. (These are the words of my grade 12 teacher)

what is the number that can replace a variable in a equation to make it a true equation? 8 letters this is not a good answer go look 4 a notha one

A number that makes an equation true is a solution. If there is more than one answer to an equation (such as an equation like): (x-2)(x+4)=0 then it is called a solution set (and in this case would be x={-4, 2}).

0 x b = 0 has more than 1 solution. This is because 0x1= 1 and 0x2= 0 does too.

add one to the problem

Given the equation 3x + 4 = 7, will there ever be more than one solution for x?

Always. Every ordered pair is the solution to infinitely many equations.