Please help I’m stuck on this question

If f(1) = 0, what are all the roots of the function f (x) = x cubed 3 x squared minus x minus 3? Use the Remainder Theorem. X =

LiRa [457]

All the roots of the provided function If f(1) is equal to the zero are -3, -1 and 1.

<h3>What is polynomial?</h3>

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The function given in the problem is,

$f(x)=x^3+3x^2-x-3$

If f(1) = 0

$f(1)=(1)^3+3(1)^2-(1)-3\\f(1)=1+3-1-3\\f(1)=0$

Thus, (x-1) is one of the factor of polynomial. Equate the polynomial equal to the zero, to find other roots as,'

$x^3+3x^2-x-3=0\\x^2(x+3)-1(x+3)=0\\(x+3)(x^2-1)\\(x+3)(x+1)(x-1)=0$

Equate all the groups to zero to find the roots as,

$x+3=0, x=-3\\x+1=0, x=-1\\x-1=0, x=1$

Hence, all the roots of the provided function If f(1) is equal to the zero are -3, -1 and 1.

Learn more about polynomial here;

brainly.com/question/24380382

5 0

3 years ago

How much does a chicken cost and duck?

Firdavs [7]

Answer:

Chicken is $8

Duck is $5

Step-by-step explanation:

Step 1: Let $x$ represent the cost of chickens and let $y$ represent the cost ducks. Since we have two unknowns, we need two equations to find them.

Step 2: The total cost of chickens Michael sold last month can be shown as $50x$ , and the total cost of ducks he sold last month can beshown as $30y$ Since these together add up to 550, we get these equations:

$50x+30y = 550$

We are also given that this month, Michael sold 44 chickens, and 36start text, 36 ducks, $532. This equaion can be expressed as:

$44x+36y=532$

Now that we have a system of the two equations, we can now go ahead and solve the two equations.

Step 3: We can now solve the system of equations by using the elimination method. Manipulate the equations so one of the variables has the same coefficients but with opposite signs.

$-6*50x+(-6)*30y\\=-300x-180y\\=-6*550\\=-3300$ $5*44x+5*36y\\=220x+180y\\=5*532\\=2660$

Now eliminate $y$

$-300x-180y=-3300\\+220x+180y=2660\\=-80x-0=-640$

When we solve the resulting equation, we obtain that $x=8$ . Then, we can substitute this into one of the original equations and solve for $y$ to obtain $y=5$ .