Form a polynomial whose real zeros and degree are given.
Zeros:
Type a polynomial with integer coefficients and a leading coefficient of 1.
Final Answer: The polynomial with integer coefficients and a leading coefficient of 1, whose real zeros are -2, 0, and 5, and degree is 3, is
Step 1 :The zeros of a polynomial are the values of x for which the polynomial equals zero. If we know the zeros of a polynomial, we can form the polynomial by multiplying factors of the form
Step 2 :The degree of the polynomial is the highest power of x in the polynomial. Since the degree is 3, and we have 3 factors, each of degree 1, we don't need to add any more factors.
Step 3 :Thus, the polynomial is
Step 4 :Simplifying this expression, we get the same polynomial
Step 5 :Final Answer: The polynomial with integer coefficients and a leading coefficient of 1, whose real zeros are -2, 0, and 5, and degree is 3, is