SOLUTION: Write an equation of the polynomial, in standard form, with roots 3,-5,2 that also pass through the point (4,54).

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Write an equation of the polynomial, in standard form, with roots 3,-5,2 that also pass through the point (4,54).      Log On


   

Question 1180559: Write an equation of the polynomial, in standard form, with roots 3,-5,2 that also pass through the point (4,54).
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


With roots 3, -5, and 2, the equation in factored form is

f%28x%29=a%28x-3%29%28x%2B5%29%28x-2%29

To determine the constant a, use the information that f(4)=54:

54=a%281%29%289%29%282%29+=+18a
a=3

The equation in factored form is

f%28x%29=3%28x-3%29%28x%2B5%29%28x-2%29

Use basic algebraic techniques to convert the equation to standard form.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
to write an equation of the polynomial, in standard form, with roots x%5B1%5D=3,x%5B2%5D=-5,x%5B3%5D=2 that also pass through the point(x,y)= (4,54), use zero product property formula
y=a%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29.....substitute given zeros and point
54=a%284-3%29%284-%28-5%29%29%284-2%29
54=a%281%29%289%29%282%29
54=18a
54%2F18=a
a=3
now go back to
y=3%28x-3%29%28x%2B5%29%28x-2%29
y=3x%5E3-57x%2B90