We want to find a polynomial given that we know its roots and a point on the graph.
We will find the polynomial:
p(x) = (183/280)*(x - 1)*(x - 1)*(x + 2)*x
We know that for a polynomial with roots {x₁, x₂, ..., xₙ} and a leading coefficient a, we can write the polynomial equation as:
p(x) = a*(x - x₁)*(x - x₂)...*(x - xₙ)
Here we know that the roots are:
- x = 1 (two times)
- x = 0
- x = -2
Then the roots are: {1, 1, 0, -2}
We can write the polynomial as:
p(x) = a*(x - 1)*(x - 1)(x - 0)*(x - (-2))
p(x) = a*(x - 1)*(x - 1)*(x + 2)*x
We also know that this polynomial goes through the point (5, 336).
This means that:
p(5) = 336
Then we can solve:
336 = a*(5 - 1)*(5 - 1)*(5 + 2)*5
336 = a*(4)*(4)*(7)*5
336 = a*560
366/560 = a = 183/280
Then the polynomial is:
p(x) = (183/280)*(x - 1)*(x - 1)*(x + 2)*x
If you want to learn more, you can read:
brainly.com/question/11536910
