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Find the zeros of the function. Enter the solutions from least to greatest.

g(x)=7x^(2)-567
lesser
x= greater
x=

Find the zeros of the function. Enter the solutions from least to greatest. $\newline$ $g(x)=7x^{2}-567$ $\newline$ lesser $x=$ greater $x=$

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Solve a quadratic equation using square roots

Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.

\newline

g(x)=7x^{2}-567

\newline

lesser

x=

greater

x=

Find the zeros: Set the function equal to zero to find the zeros. $\newline$ g(x) = $7x^2 - 567 = 0$
Factor out the common factor: Factor out the common factor of $7$ from the equation. $7(x^2 - 81) = 0$
Apply the zero product property: Apply the zero product property, which states that if a product of factors equals $0$ , then at least one of the factors must be $0$ . $\newline$ $x^2 - 81 = 0$
Factor further using difference of squares: Recognize that $x^2 - 81$ is a difference of squares and can be factored further. $\newline$ $(x + 9)(x - 9) = 0$
Set each factor equal to zero: Set each factor equal to zero and solve for $x$ . $x + 9 = 0$ or $x - 9 = 0$
Solve for x in the first equation: Solve the first equation for x. $\newline$ $x + 9 = 0$ $\newline$ $x = -9$
Solve for x in the second equation: Solve the second equation for x. $\newline$ $x - 9 = 0$ $\newline$ $x = 9$

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