What is considered a rational zero?
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What is considered a rational zero?
A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.
When can you use the Rational Zero Theorem?
The Rational Zeros Theorem states: If P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P( ) = 0), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x). We can use the Rational Zeros Theorem to find all the rational zeros of a polynomial.
Why is rational zero theorem useful?
If the leading coefficient of a polynomial is 1, then the factors of the constant themseveles are the possible rational zeros of f(x). The rational zero theorem helps us to find the zeros of a polynomial function only if it has rational zeros. The rational zero theorem helps in solving polynomial equations.
What is P and q in the Rational Zero Theorem?
In the rational zero theorem, p and q stand for all potential rational roots of a polynomial. p represents all positive and negative factors of the constant of the polynomial whereas q represents all positive and negative factors of the leading coefficient of the polynomial.
How do you find rational zeros of a polynomial?
Here are the steps:
- Arrange the polynomial in descending order.
- Write down all the factors of the constant term. These are all the possible values of p.
- Write down all the factors of the leading coefficient.
- Write down all the possible values of .
- Use synthetic division to determine the values of for which P( ) = 0.
Why the Rational Zeros Theorem does not guarantee finding zeros of a polynomial function?
Because zeros can repeat. Explain why the Rational Zero Theorem does not guarantee finding zeros of a polynomial function. It is possible that the polynomial function does not have any rational zeros. Irrational and imaginary zeros will not appear on the list of possible rational zeros that you get from that theorem.
What is a zero polynomial give example?
A zero polynomial can have an infinite number of terms along with variables of different powers where the variables have zero as their coefficient. For example: 0x2 + 0x + 0. The zero polynomial function is defined as y = P(x) = 0 and the graph of zero polynomial is the x-axis.
