Question 524522
how do you find a polynomial of degree 4 with -2 as a zero
of multiplicity 2 and 0 and 3 as zeros of multiplicity 1.
<pre>
Make a row of equations with x = each of the zeros, 
as many times as their multiplicities:

      x = -2,       x = -2,    x = 0,        x = 3

Get 0 on the right of each equation:

  x + 2 = 0     x + 2 = 0      x = 0,    x - 3 = 0  

Write the product of all the left sides:

         (x + 2)(x + 2)(x)(x - 3) = 0

Multiply them all together:

           (x<sup>2</sup> + 4x + 4)(x<sup>2</sup> - 3x) = 0

x<sup>4</sup> - 3x<sup>3</sup> + 4x<sup>3</sup> - 12x<sup>2</sup> + 4x<sup>2</sup> - 12x = 0 

Collect like terms

              x<sup>4</sup> + x<sup>3</sup> - 8x<sup>2</sup> - 12x = 0 

Set P(x) = the left side:

          P(x) = x<sup>4</sup> + x<sup>3</sup> - 8x<sup>2</sup> - 12x

Edwin</pre>