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nekit [7.7K]
4 years ago
14

Which are the real zeros of this function? f(x) = x3 – 6x2 – 16x

Mathematics
1 answer:
murzikaleks [220]4 years ago
5 0
To find the zeros of the function f(x)= x^{3} -6x^{2}-16x we need to factorize the expression.

f(x)= x^{3} -6x^{2}-16x =x(x^{2} -6x-16 )

a nice way to factorize x^{2} -6x-16, if possible, is by completing the square as follows:

x^{2} -6x-16 =x^{2} -2*3x+ (3)^{2}-(3)^{2} -16

=(x^{2} -2*3x+ (3)^{2})-9-16= (x-3)^{2}-25= (x-3)^{2}- 5^{2}

now we use the difference of squares formula a^{2} - b^{2} =(a+b)(a-b):

(x-3)^{2}- 5^{2}=[(x-3)+5][(x-3)-5]=[x+2][x-8]


finally, we combine the results:

f(x)=x(x+2)(x-8)

the zeros of f, are the values of x which make f(x)=0,

they are x=0, x=-2 and x=8


Answer: {-2, 0, 8}

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