So when Helmholtz recognized that thought moves at a finite rate, faster than a bird but slower than sound, he missed a fundamental difference between the brain and a telegraph. In our heads, speed is not always the most important thing. Sometimes what really matters is timing.
A solution of a quadratic equation is a value of the variable that makes the equation true. Many quadratic equations. can be solved by factoring and using the zero-factor property. The Zero-Factor Property: When the product of two real numbers is 0, at least one of them is 0.
The zeros of a polynomial function p(x) are the x-values that yield 0 as the function's value. I.e. The zeros of the polynomial p(x) are the roots, or solutions, to the equation p(x) = 0. Zeros are also called the x-intercepts of the polynomial, or points where the graph of the polynomial touches the x-axis. From the factor theorem, we know that when c is a zero of the polynomial p(x), then x - c is a factor of p(x). The multiplicity of the number of factors of x - c in the linear factorization of p(x). Find the zeros and multiplicity of each polynomial. Mouse over the blacked out entries to check your the answer.