Question

Write the polynomial form given the leading coefficient

and the zeros of the function.
1. Leading coefficient: -1; roots: 1, 1+73, 1 - 3

someone help please

Answer 1

For a polynomial of any degree, with roots x₁, x₂, ...., xₙ and a leading coefficient A, we can write it as:

p(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)

In this case, we have:

Leading coefficient = -1

Roots : 1, 1 + 73, 1 - 3

Then the polynomial will be:

p(x) = -1*(x - 1)*(x - (1 + 73))*(x - (1 - 3))

= -1*(x - 1)*(x - 74)*(x + 2)

Now, if the roots are:

1, 1 + 73*i, 1 - 3*i

then:

p(x) = -1*(x - 1)*(x - 1 - 73*i)*(x - 1 + 3*i)