Find polynomial function with the following zeros

Question

write the polynomial function of least degree with a leading coefficient of 1 and has the following zeros. 7, -4, (sq root 3)

Answer 1

Define factors that have the zeros:

 

(x - 7)

[x - (-4)] = (x + 4)

(x ± √3)  [Include both +√3 and -√3, assuming you want rational coefficients in the polynomial.]

 

Multiply the factors and also multiply by a coefficient a ≠ 0

 

p(x) = a(x - 7)(x + 4)(x - √3)(x + √3)

 

The leading coefficient is a, so a = 1 in this problem.

 

p(x) = (x - 7)(x + 4)(x - √3)(x + √3)

 

You can expand this as a polynomial of degree 4 to finish the solution.