The function f ( x ) = x ^3 + 2x^2− 5 x − 6 has a root at 2. name all roots of this function.

a.-2, -1, -3

b.2, 1, 3

c.2, -1, -3

d.-2, 1, 3

sub x=1 into f(x),

remainder= 1^3+2(1)^2-5(1)-6= -8

since remainder≠0, x=1 is not a root of the function

sub x=-1,

remainder = (-1)^3+2(-1)^2-5(-1)-6= 0

by remainder theorem,

x=-1 is a root of f(x)

hence, the correct ans is c

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