What are the possible number of positive real, negative real, and complex zeros of. f(x) = 4x3 + x2 + 10x - 14.

1 sign change when x=1, there is 1 positve root

2 sign changes when x = -1. there are 2 possible negative roots

since complex roots come in 2s, there might be 0 negative roots, and 2 complex roots

close, but we cant say for sure that there are 0 or 2 negative roots; or 0 or 2 complex roots

Positive Real: 1

Negative Real: 0, or 2

Complex: 0, or 2

Positive roots = 1

Negative real root =0 or 2

complex roots=0 or 2

Step-by-step explanation:

Given cubic polynomial f(x) =

By Descartes rules of signs

as this polynomial is already arranged in descending order and has only 1 sign change which means it has 1 positive real root.

Now change signs of coefficients of odd powered terms we get

then we have 2 sign changes which gives 2 or zero negative real roots .

For complex roots , we know that it is a cubic polynomial i.e. it has exactly 3 roots and complex roots always occur in pair, Therefore it will have zero or 2 complex roots.

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.

step-by-step explanation: