square 1 The polynomis of degree 4, P(z) has a not of m z=0 and z=-1 . It goes through the point 6. Find a formula for P(z) P(z)= square

Question

square 1 The polynomis of degree 4, P(z) has a not of m z=0 and z=-1 . It goes through the point 6. Find a formula for P(z) P(z)= square

Answer 1

To find the polynomial \( P(z) \) of degree 4 with the given roots and point, we can use the fact that if

and

are roots, then

and

are factors of the polynomial. Additionally, since

is a root,

is also a factor.Given that the polynomial passes through the point (6, 0), we can use this information to determine the constant factor.The polynomial can be written as:

To find the constant

, we use the fact that the polynomial passes through the point (6, 0). This means that when

, \( P(6) = 0 \).Substituting

into the polynomial equation, we get:

Simplifying the equation, we have:

Since the equation is true for any value of

, we can choose

for simplicity.Therefore, the polynomial \( P(z) \) is:

Expanding the factors, we get:

So, the final answer is:

Question

square 1 The polynomis of degree 4, P(z) has a not of m z=0 and z=-1 . It goes through the point 6. Find a formula for P(z) P(z)= square

Solution

Resposta