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anemone
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If $P(0)=3$ and $P(1)=11$ where $P$ is a polynomial of degree 3 with integer coefficients and $P$ has only 2 integer roots, find how many such polynomials $P$ exist?
anemone said:If $P(0)=3$ and $P(1)=11$ where $P$ is a polynomial of degree 3 with integer coefficients and $P$ has only 2 integer roots, find how many such polynomials $P$ exist?
The Polynomial Challenge: Find # of Int Roots of Degree 3 w/ Coeffs is a mathematical problem that involves finding the number of integer roots of a polynomial equation with a degree of three and given coefficients.
A polynomial equation is an algebraic equation that contains one or more terms with variables raised to positive integer powers. It can have multiple terms and may also include constants and coefficients.
To find the number of integer roots of a polynomial equation, you can use the Rational Root Theorem, which states that any rational root of a polynomial equation is a factor of the constant term divided by the leading coefficient. By testing the possible rational roots, you can determine the number of integer roots.
The degree of a polynomial equation is the highest exponent of the variable in the equation. For example, in the equation 3x^2 + 5x + 2, the degree is 2.
Finding the number of integer roots is important in polynomial equations because it helps determine the solutions or the x-intercepts of the equation. These integer roots are also known as rational roots and can provide valuable information about the behavior and properties of the polynomial function.