2 years ago
Find a polynomial f(x) of degree 5 that has the following zeros.
-9, 5, -7, 4, 8
f(x)=
-9, 5, -7, 4, 8
f(x)=
1 Answers
Best Answer
ub40ticketsbirmingham Staff answered 2 years ago
ub40ticketsbirmingham Staff answered 2 years ago
Step 1
The Factor Theorem for a non-zero polynomial p states that, if c is any real number, then,
c is a zero of p iff (x-c) is a factor of p(x)
Step 2
The polynomial f of degree 5 with the given zeros can be formulated as follows. The degree of the factors must add up to 5.
f(x)=(x-(-9))(x-5)(x-(-7))(x-4)(x-8)
f(x)=(x+9)(x-5)(x+7)(x-4)(x-8)
The Factor Theorem for a non-zero polynomial p states that, if c is any real number, then,
c is a zero of p iff (x-c) is a factor of p(x)
Step 2
The polynomial f of degree 5 with the given zeros can be formulated as follows. The degree of the factors must add up to 5.
f(x)=(x-(-9))(x-5)(x-(-7))(x-4)(x-8)
f(x)=(x+9)(x-5)(x+7)(x-4)(x-8)