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Find the zeros of the function g(x)=4x2−484g(x)=4x^2-484 Enter the solutions from least to greatest.

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Full solution

Q. Find the zeros of the function g(x)=4x2−484g(x)=4x^2-484 Enter the solutions from least to greatest.
  1. Set Function Equal to Zero: Set the function equal to zero to find its zeros.\newlineg(x)=4x2−484=0g(x) = 4x^2 - 484 = 0
  2. Factor Out Common Factor: Factor out the common factor of 44 from the equation.4(x2−121)=04(x^2 - 121) = 0
  3. Recognize Difference of Squares: Recognize that x2−121x^2 - 121 is a difference of squares and can be factored further.\newline(x2−121)=(x+11)(x−11)(x^2 - 121) = (x + 11)(x - 11)
  4. Set Factors Equal to Zero: Set each factor equal to zero to solve for xx.x+11=0x + 11 = 0 or x−11=0x - 11 = 0
  5. Solve for x: Solve each equation for x.\newlinex=−11x = -11 or x=11x = 11

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