Write a polynomial with zeros of 4, -1, 0.

Question

I forgot how to do this. I just need help. So how would I do this problem??

 

Answer 1

P(x) = [ x - (4) ][ x - (-1)][ x - (0)] = (x-4)(x+1)x = (x² + x -4x -4)x = (x² -3x -4)x = x³ -3x² -4x

 

Remember, Ella, that the zeros (a.k.a. roots) of P(x) are the x's that make P(x) equal to zero !

P(0) = 0; P(-1) = 0 and P(4) = 0 for this specific P(x) = x³ - 3x² - 4x

 

Review your lessons/notes. Stop "forgetting how to do this" !   :)

 

Good Luck for your Final ...

Answer 2

Ella,

 

What are the zeros of x² - 4 ?

 

Set x² - 4 = 0.

 

Factoring...

 

(x+2)(x-2) = 0

 

x = 2, -2.

 

Now what if we worked backwards? Say we were told there were zeros at 2 and -2.

 

Then we would write

 

(x+2)(x-2) = 0, since plugging 2 and -2 into this equation give 0.

 

Try using this logic on your problem. The only complicating part may be that one of your zeros is 0.

 

To see how you might include 0 as a factor, consider this question: What are the zeroes of x(x+2)(x-2) = 0? 2, -2, and...?

 

Please leave a comment if you would like more help.

 

Best,

Bryce