Degree 3 polynomial with integer coefficients with zeros -7i and 45 Select one: a. F (x) = 25x3 - 75x2 + 296x - 112 b. F (x) = 25x3 - 5x2 - 264x + 112 c. F (x) = 5x3 - 4x2 - 245x + 196 d. F (x) = 5x3 - 4x2 + 245x - 196

The correct option is (d)

The required polynomial is

F(x)=5x³- 4x²+245x-196

Step-by-step explanation:

Conjugate root theorem:

If the complex number a+ib is a root of a polynomial P(x) with real coefficient in one variable,then the complex conjugate a-ib is also a root of P(x).

Given that,

Degree 3 polynomial with integer coefficients with zeros -7i and .

Since -7i is complex root of the required polynomial.

Then 7i is also a root of the required polynomial.

Then,

               [ (a+b)(a-b)= a²-b²]

                   [ since i² = -1]

      =5x³+245x-4x²-196  [ Multiply by 5]

     =5x³- 4x²+245x-196

The required polynomial is

F(x)=5x³- 4x²+245x-196

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

step-by-step explanation: