Polynomial function in standard form

Question

Write a polynomial function in standard form with zeros -1, -1, 6.

Answer 1

Hi Dina;

 

If x=n is a zero of p(x), then (x-n) is a factor of p(x)

 

p(x) = a(x-(-1))(x-(-1))(x-6)

where a is some number

 

p(x) = a(x+1)²(x-6)

 

From here, since we had no requirement for a first coefficient,

you can let a=1.  If you had required, for example, the 1st

coefficient to be 3 it would be p(x) = 3(x+1)²(x-6)

 

p(x) = (x² + 2x + 1)(x-6)

 

p(x) = x³ - 6x² + 2x² - 12x + x - 6

 

p(x) = x³ - 4x² - 11x - 6

 

 

check:  x = -1, p(x) = 0

(-1)³ - 4(-1)² - 11(-1) - 6 = 0

-1 -4 + 11 - 6 = 0

-11 + 11 = 0

0 = 0    yes

 

x = 6, p(x) = 0

6³ -4(6)² - 11(6) - 6 = 0

216 - 144 - 66 - 6 = 0

216 - 216 = 0    yes

 

Questions?