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Example 1
Which of the following polynomial equations has the solution set {-5,-3,-1,0,3}?
- $(x-5)(x-1)(x^2+9)=0$
- $(x+5)(x+1)(x^2+9)=0$
- $x(x-5)(x-1)(x^2+9)=0$
- $(x+5)(x+1)(x^2-9)=0$
- $x(x+5)(x+1)(x^2-9)=0$
Solution
- We first start by writing a polynomial as a product of linear factors using the given solution set as follows
$(x+5)(x+3)(x+1)(x-0)(x-3)$
- Note that $(x-3)(x+3) = x^2-9$, hence the equation with the given solutions may be given as follows
$x(x+5)(x+1)(x^2-9)=0$
Answer E
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