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

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

there are no multiple choices