Find a polynomial with real coefficients that has the given zeros. -1 and 3 - 4i One such polynomial P(x) can be defined as P left parenthesis x right parenthesis equals x cubed minus 5 x squared plus _ _ _ x plus 25. What coefficient belongs in the blank?

29

Step-by-step explanation:

If the real coefficients that has the given zeros are -1 and 3 - 4i, this means -1 and 3-4i are both roots of the polynomial. If their equivalent polynomial function is given as;

P(x) = x³-5x²+kx+25 = 0

Where k is the unknown coefficient.

To get the value of k, we will substitute any of the zero values of the polynomial into the polynomial to have;

P(-1) = (-1)³-5(-1)²-k+25 = 0

P(-1) = -1+5-k+25

P(-1) = 29-k = 0

29-k = 0

k = 29

The coefficient that belongs to the blank is 29

x+y=90

x=30-y=x

step-by-step explanation:

if you understand you will get the answer

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: