5,2,square root 3 polynomial function

Question

I need to find polynomial functions for 5,2 and squareroot of 3

Answer 1

Hi, Annna.  

 

Let me do a similar problem for you.  You can follow along with my work and solve your problem.  

 

Let's say I wanted to find a polynomial with roots 6, 8, and the square root of 7.  First, I would start by recognizing that that if the square root of 7 is a root, so is negative square root of 7.  Next, I would find the four factors of my polynomial by subtracting each root from x, like this: 

 

(x-6)(x-8)(x-√7)(x--√7)

 

Because subtracting a negative is like adding a positive, I can simplify a little: 

 

(x-6)(x-8)(x-√7)(x+√7)

 

Now I need to multiply everything out to get my polynomial in standard form.  I'll just "FOIL" the first two factors together and "FOIL" the second two facotrs together to get:

 

(x²-14x+48)(x²+7)

 

Now I need to multiply the two factors above.  I get: 

 

x⁴-14x³+55x²-98x+336

 

I hope this helps!  You can do all of the same steps using the numbers in your problem.  Good luck!