the roots are 1, - 1/3, - 3 1/2 and 3 1/2
No. The square roots of 2, 3 and 5, for a start, are not rational.
No, they are not.
Rational roots
Yes. Both square roots of 36 are rational.
No, the vast majority are not.
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.
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.
Rational zero test cannot be used to find irrational roots as well as rational roots.
-39 has no rational roots.
A rational expression is not defined whenever the denominator of the expression equals zero. These will be the roots or zeros of the denominator.
The square roots are irrational.
No. The square roots of 2, 3 and 5, for a start, are not rational.
The square root of 16 is rational. The answer would be 4, so, yes; they can be rational.
The square roots are rational.
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.
I do not believe that there are any rational roots.
Some square roots are rational but the majority are not.