SOLUTION: Write a polynomial in factored and standard form: P is of degree 2; P(0) = 14; zeros : 1 and -2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a polynomial in factored and standard form: P is of degree 2; P(0) = 14; zeros : 1 and -2      Log On


   

Question 265254: Write a polynomial in factored and standard form:
P is of degree 2; P(0) = 14; zeros : 1 and -2
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Lets look at the zeros first: 1 and -2
x = 1 and x = -2
set each equal to zero to get
(x-1) = 0 and (x+2) = 0
multiply to get
(x-1)(x+2) = 0
so far,
P(x) = x^2-x - 2
next we see
P(0) = 14
substitute to get
14 = 0-2-2
which is
14 = -2
what do you have to do to the -2 to make it 14?
ANSWER: multiply by -7
So, p(x) becomes
P(x) = -7x^2 + 7x + 14