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We know an equation in one variable has solutions/roots equivalent to its degree, then why an equation with power 0 has infinite roots, i.e. x^0 = 0 has infinite no. of solution. Why is it so?

We know an equation in one variable has solutions/roots equivalent to its degree, then why an equation with power 0 has infinite roots, i.e. x^0 = 0 has infinite no. of solution. Why is it so?

Grade:11

2 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Deepankar,

 

This is very interesting to hear.

But please note that, the statement you have mentioned is applicable to only powers of positive integers.

 

For Example x-2 = 4, still has two roots (It does not make sense to say it has -2 number of roots).

Coming to your case.

x0 = 0, infact has no roots, in real numbers (it cannot have infinite roots).

Infact it is x0 = 1 is what will have infinite roots.

 

Imagine it like this:

Consider the log 1 to the base of some positive number "x" ( not equal to 1).

As log(1) is always 0, to any positive base, this will have infinite solutions.

 

Hence x^0 = 1 has infinite solutions.

 

Best Regards,

Ashwin (IIT Madras).

Swapnil Saxena
102 Points
10 years ago

X^0=0 has no roots however x^0=1 has infinite roots. Infact every real no. excluding 0 is one of the equations.

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