SOLUTION: Find a polynomial satisfying the following conditions: f has degree 3;the roots of f are precisely 2,3,4;the leading coefficient is 2.

Question 814185: Find a polynomial satisfying the following conditions:
f has degree 3;the roots of f are precisely 2,3,4;the leading coefficient is 2.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If "r" is a root of a polynomial, then (x - r) is a factor of the polynomial. So with the three given roots and the leading coefficient we can immediately write a factored version of the desired function:
f(x) = 2(x-2)(x-3)(x-4)

All that is left is to multiply this out. Since this is all multiplication we can multiply in any order. I'll start by using FOIL on the last two factors:
f(x) = 2(x-2)(x*x+x*(-4)+(-3)*x+(-3)(-4))
Simplifying...

Multiplying the first two factors:

One more multiplication:

Simplifying...

or
RELATED QUESTIONS
Find an nth degree polynomial function with real coefficients, a leading coefficient of 1 (answered by greenestamps,ikleyn)

Find an nth degree polynomial satisfying the given conditions: n=3; 2 and 2-3i are... (answered by ReadingBoosters)

Find an nth degree polynomial function with real coefficients satisfying the given... (answered by josgarithmetic)

Find the nth-degree polynomial function with real coefficients satisfying the given... (answered by ikleyn)

Find an nth-degree polynomial function with real coefficient satisfying the given... (answered by MathLover1)

Find an nth-degree polynomial function with real coefficients satisfying the given... (answered by stanbon)

find a fourth degree polynomial function with real coefficients satisfying the given... (answered by jsmallt9)

find the nth degree polynomial function with real coefficients satisfying the given... (answered by josgarithmetic)

Find an nth degree polynomial function with real coefficients satisfying the given... (answered by stanbon)