Respuesta :
Answer:
Therefore,
A polynomial with integer coefficients and a leading coefficient of 1,
[tex]x^{3}-44x^{2}-605x=0[/tex]
Step-by-step explanation:
Given:
Zeros:
−11, 0, 55;
degree: 3
To Find:
Type a polynomial with integer coefficients and a leading coefficient of 1.
Solution:
For a Polynomial degree will decide the number of zeros,
Degree: n indicates "n" number of zeros.
Here, degree: 3 indicates 3 zeros
Let for a Polynomial of degree 3 and ZEROS: a , b and c. then the polynomial is given as
[tex]P(x)=(x-a)(x-b)(x-c)=0[/tex]
Here Zeros are
a = -11,
b = 0,
c = 55
Therefore,
[tex]P(x)=(x-(-11))(x-0)(x-55)=0\\\\(x+11)x(x-55)=0\\\\x(x^{2}-44x-605)=0\\\\x^{3}-44x^{2}-605x=0[/tex] ...Which is the required Polynomial
Therefore,
A polynomial with integer coefficients and a leading coefficient of 1,
[tex]x^{3}-44x^{2}-605x=0[/tex]
