SOLUTION: Find two different polynomials j(x) and g(x) such that the degree of each polynomial is greater than 1 and j(5) = g(5) = 0. I don't even know where to start.

Algebra ->  Functions -> SOLUTION: Find two different polynomials j(x) and g(x) such that the degree of each polynomial is greater than 1 and j(5) = g(5) = 0. I don't even know where to start.       Log On


   

Question 892677: Find two different polynomials j(x) and g(x) such that the degree of each polynomial is greater than 1 and j(5) = g(5) = 0. I don't even know where to start.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
This allows many possible polynomials j and g.
Needing a root to be 5, each function would have a binomial factor x-5. Generally, you can have both j and g in degree 2, which is greater than degree 1.

g%28x%29=%28x-m%29%28x-5%29 and j%28x%29=%28x-p%29%28x-5%29 and that m, and p, are any real numbers. You can also include a factor for each polynomial, also of real numbers.

If k and h are both any real numbers NOT equal to zero, then you can have
g%28x%29=k%28x-m%29%28x-5%29 and j%28x%29=h%28x-p%29%28x-5%29.

The problem specified that each degree must be greater than 1; and my general example used degree 2 for both functions. You can choose higher degrees if desired. You can choose something like j%28x%29=%28kx%5E2-bx%2Bc%29%28x-5%29 for real numbers k, b, c, and recognize that j(x) is in degree 3. This still has a root of 5.