Algebra-2

According to the Rational Root Theorem, for a polynomial equation , the possible rational roots are of the form , where  is a factor of the constant term  and  is a factor of the leading coefficient .

For the equation , the leading coefficient is 10 and the constant term is -10.

Factors of -10 are ±1, ±2, ±5, ±10.

Factors of 10 are ±1, ±2, ±5, ±10.

So the possible rational roots are ±1/1, ±1/2, ±1/5, ±1/10, ±2/1, ±2/2 (which simplifies to ±1), ±2/5, ±2/10 (which simplifies to ±1/5), ±5/1, ±5/2, ±5/5 (which simplifies to ±1), ±5/10 (which simplifies to ±1/2), ±10/1, ±10/2 (which simplifies to ±5), ±10/5 (which simplifies to ±2), ±10/10 (which simplifies to ±1).

Now we test these possible roots one by one.

Testing :

Substitute  into the equation: .

Testing :

Substitute  into the equation:

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