Answer :

A double zero occurs in a polynomial when a factor is repeated, or in other words, squared. Since the polynomial has double zeros, then, we get

[tex]f(x)=(x+3)^2(x-4)^2[/tex]

By expanding this result, we have

[tex]f(x)=(x^2+6x+9)(x^2-8x+16)[/tex]

which gives

[tex]f(x)=x^4-8x^3+16x^2+6x^3-48x^2+96+9x^2-72x+144[/tex]

By combining similar terms, we have

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