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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
9 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
9 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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