Use the remainder theorem to determine which number is a root of f(x) = 2x3 + x2 - 7x + 4.

The Roots of f(x) are

x=1

x=

and x=

Step-by-step explanation:

Given function f(x)=

We know that

A. The sum of coefficient of polynomial is zero then, (x-1) is one of root of polynomial

f(1)=0

B. The difference of sum of coefficient of odd term and sum of coefficient of even term of polynomial is zero then, (x+1) is one of root of polynomial

f(-1)=0

Let x=1

f(1)=

f(1)=2+1-7+4=0

Therefore, (x-1) is one of root.

Let x=(-1)

f(1)=

f(1)=-2+1+7+4=10

Therefore, (x-1) is not one of root.

Using Remainder theorem:

Dividing (x-1) on both the side.

For 2x^{2}+3x-4

a=2,b=3 and c=(-4)

D=

D=

D=

x= and x=

x= and x=

x= and x=

Thus,

The Roots of f(x) are

x=1

x=

and x=

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

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