Given:
The zeroes of the polynomial are -11 and 2.
The objective is to find a polynomial function P(x) with leading coefficient 1, least possible degree.
Consider the given zeroes as, x=-11 and x=2.
Now the zeroes can be written as,
[tex](x+11)(x-2)=0[/tex]Now, multiply the terms using algebraic identitites,
[tex]\begin{gathered} x^2-2x+11x-22=0 \\ x^2+9x-22=0 \end{gathered}[/tex]Here, the leading coefficient is 1. The real coefficients are 1, 9, -22.
Hence, the required polynomial is obtained.
