What are the zeros of the function g(x) = (x+5)(x-2)(x+1)

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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The zeroes of the function are all the roots of the equation (x+5)(x-2)(x+1) = 0, putting g(x) = 0.

Since the expression of the function is a product, and, according to the rule, a product is zeri if at least one factor is zero, we'll set each factor as zero.

x + 5 = 0

We'll subtract 5 both sides:

x = -5

The first zero of g(x) is x = 5.

x - 2 = 0

We'll add 2 both sides:

x = 2

The second zero of g(x) is x = 2.

x+1 = 0

We'll subtract 1 both sides:

x = -1

The third zero of g(x) is x = -1.

Since the polynomial g(x) is of 3rd order, we cannot have more than 3 zeroes.

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neela | High School Teacher | (Level 3) Valedictorian

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g(x) =(x+5)(x-2)(x+1).

To find the zeros of the  g(x).

We know that the zeros of a function g(x)  are the set of values of x for which g(x) evaluates to zero.

If x1 is a zero g(x), then if we substitute x1 for x in g(x) , then g(x1) = 0.

Therefore if we  can write g(x) in the form g(x) = (x-a)(x-b)(x-c), then g(a) = (a-a)(a-b)(a-c).  Or g(a) = 0*(a-c)(a-c) = 0. That proves a zero of g(x).

Similarly  if g(x) = (x-a)(x-b)(x-c), then g(b) = (b-a)(b-b)(b-c) = 0 , and g(c) = (c-a)(c-b)(c-c) = 0.

Therefore ifg(x) = (x-a)(x-b)(x-c), then x =a ,x = b and x= c are the zeros of g(x).

In this case g(x) = (x+5)(x+1)(x-2). So a = -5, b = -1 c = 2 are the  zeros of g(x). The zeros are also the solutions of each factor of g(x) equated to zero:  x+5 = 0 , x-2 = 0 , x-2 = 0

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william1941 | College Teacher | (Level 3) Valedictorian

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The zeroes of a function are values of x for which the values of the function is equal to zero.

Here we have: g(x) = (x+5)(x-2)(x+1)

Now if g(x)= 0

=>(x+5)(x-2)(x+1) = 0

=> x+5 = 0 or x -2 =0  or x +1 =0

=> x = -5 or x = 2 or x = -1

Therefore the zeroes of the function are x = -5, x =2 and x = -1.

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