Question

Write a polynomial of least degree with roots 9 and 5.Write your answer using the variable x and in standard form with a leading coefficient of 1. - See more at: http://www.ixl.com/math/algebra-2/write-a-polynomial-from-its-roots#sthash.5LOlNmjW.dpuf

Answer 1

a polynomial with roots of 9 and 5, just means

x = 9 => x-9 = 0 => (x -9) = 0
x = 5 => x-5 = 0 => (x-5) =0

the polynomial can be obtained by multiplying both ROOTS

Answer 2

So we know that the leading co-efficient is \(1\) and that we have roots \(x=9\), and \(x=5\)
We know that for an equation with \(n\) number of roots, the least degree would be \(n\). Since we have two roots, we are dealing with a quadratic! So then we know that the equation for a quadratic with a leading co-efficient \(a\) and roots \(x=r\) and \(x=s\) is:
\[y=a(x-r)(x-s)\]
When we substitute, we end up with:
\[\eqalign{
y&=1(x-9)(x-5) \\
y&=(x-9)(x-5) \\
y&=x^2-5x-9x+45 \\
y&=x^2-14x+45 \\
}\]