determine the total number of roots of each polynomial function using the factored form.\n$f(x)=(x + 1)(x…
determine the total number of roots of each polynomial function using the factored form.\n$f(x)=(x + 1)(x - 3)(x - 4)$\n$f(x)=(x + 5)^3(x - 9)(x + 1)$\n$f(x)=(x - 6)^2(x + 2)^2$
Answer
Explanation:
Step1: Recall root - counting rule
The number of roots of a polynomial in factored form $f(x)=(x - r_1)^{n_1}(x - r_2)^{n_2}\cdots(x - r_k)^{n_k}$ is the sum of the exponents $n_1 + n_2+\cdots + n_k$.
Step2: Analyze $f(x)=(x + 5)^3(x - 9)(x + 1)$
The exponents of the factors are 3, 1, and 1.
Step3: Calculate the number of roots
$3+1 + 1=5$.
Answer:
5