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How can one find all rational roots of a polynomial equation?

To find all rational roots of a polynomial equation, you can use the Rational Root Theorem. This theorem states that any rational root of a polynomial equation in the form of (anxn an-1xn-1 ... a1x a0 0) must be a factor of the constant term (a0) divided by a factor of the leading coefficient (an). By testing these possible rational roots using synthetic division or polynomial long division, you can determine which ones are actual roots of the equation.


What is the rational root theroem?

In algebra, the rational root theorem (or rational root test, rational zero theorem or rational zero test) states a constraint on rational solutions (or roots) of a polynomialequationwith integer coefficients.If a0 and an are nonzero, then each rational solution x, when written as a fraction x = p/q in lowest terms (i.e., the greatest common divisor of p and q is 1), satisfiesp is an integer factor of the constant term a0, andq is an integer factor of the leading coefficient an.The rational root theorem is a special case (for a single linear factor) of Gauss's lemmaon the factorization of polynomials. The integral root theorem is a special case of the rational root theorem if the leading coefficient an = 1.


Can the rational zero test be used to find irrational roots as well as rational roots?

Rational zero test cannot be used to find irrational roots as well as rational roots.


What are all the possible rational roots of -39?

-39 has no rational roots.


How do you determine the values for which a rational expression is undefined?

A rational expression is not defined whenever the denominator of the expression equals zero. These will be the roots or zeros of the denominator.


Is The square root of 0.151 rational or irrational?

The square roots are irrational.


Are square roots always rational?

No. The square roots of 2, 3 and 5, for a start, are not rational.


Can square roots be rational?

The square root of 16 is rational. The answer would be 4, so, yes; they can be rational.


Is the square root of 0.0625 rational or irrational?

The square roots are rational.


How do you foil a quartic?

A quartic equation can be factored by grouping or using a substitution method. You can also use the rational root theorem to find potential rational roots and factorize the quartic equation accordingly. Alternatively, you can use numerical methods or technology to approximate the roots.


What are the rational roots of 3x3 plus x2-8x plus 6?

I do not believe that there are any rational roots.


Is the square root are rational numbers?

Some square roots are rational but the majority are not.