Question

Which of the following functions has the same zeros as the graph below?

Answer 1

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The given graph have four zeros at x = -3 , 0 , 2 , 7
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f(x) = x³ + x² -6x
The function f(x) is polynomial has degree = 3
so, it has only 3 zeros
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g(x) = (x²+x-6)(x²-7x)   ⇒  By factoring
⇒  By factoring
∴ g(x) = x(x-7)(x+3)(x-2)
∴ g(x) has zeros  at x = -3 , 0 , 2 , 7
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h(x) = x(x-7)(x+3)(x-2)
h(x) has zeros  at x = -3 , 0 , 2 , 7
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m(x) = (x³-4x²-21x)(x-2)
⇒  By factoring
∴ m(x) = x(x-7)(x+3)(x-2)
∴ m(x) has zeros  at x = -3 , 0 , 2 , 7
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n(x) = x²-9x+14
The function f(x) is polynomial has degree = 3
so, it has only 3 zeros
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p(x) = x(x+2)(x-3)(x+7)
∴ p(x) has zeros  at x = 3 , 0 , -2 , -7
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By comparing zeros of the given graph to zeros of the functions
The result will be:
         The functions that have the same zeros as the graph are
                                g(x) , h(x) and m(x)