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What are the roots of the polynomial equation?

[tex]\[ \frac{1}{2} x(x-7)(x+9)=0 \][/tex]

Select each correct answer.

A. [tex]$-9$[/tex]

B. [tex]$-7$[/tex]

C. [tex]$-\frac{1}{2}$[/tex]

D. [tex]$0$[/tex]

E. [tex]$\frac{1}{2}$[/tex]

F. [tex]$7$[/tex]

G. [tex]$9$[/tex]

Sagot :

GinnyAnswer
To find the roots of the polynomial equation:

[tex]\[ \frac{1}{2} x(x-7)(x+9)=0 \][/tex]

we need to set each factor of the equation equal to zero and solve for \( x \). This can be done step by step as follows:

1. The first factor is \( \frac{1}{2} x \). Setting this equal to zero:

[tex]\[ \frac{1}{2} x = 0 \][/tex]

Solving for \( x \):

[tex]\[ x = 0 \][/tex]

2. The second factor is \( x - 7 \). Setting this equal to zero:

[tex]\[ x - 7 = 0 \][/tex]

Solving for \( x \):

[tex]\[ x = 7 \][/tex]

3. The third factor is \( x + 9 \). Setting this equal to zero:

[tex]\[ x + 9 = 0 \][/tex]

Solving for \( x \):

[tex]\[ x = -9 \][/tex]

Therefore, the roots of the polynomial equation \( \frac{1}{2} x(x-7)(x+9)=0 \) are:

[tex]\[ -9, 0, 7 \][/tex]

So the correct answers are:

[tex]\[ -9, 0, 7 \][/tex]
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