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Find the zeros of the function. Enter the solutions from least to greatest. {:[h(x)=-6x^(2)+384],[" lesser "x=◻],[" greater "x=◻]:}

Find the zeros of the function. Enter the solutions from least to greatest.\newlineh(x)=−6x2+384 h(x) = -6x^{2} + 384 , lesser x=□ \text{lesser } x = \square , greater x=□ \text{greater } x = \square

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Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.\newlineh(x)=−6x2+384 h(x) = -6x^{2} + 384 , lesser x=□ \text{lesser } x = \square , greater x=□ \text{greater } x = \square
  1. Identify quadratic function: Identify the quadratic function and set it equal to zero to find its zeros.\newlineWe have the quadratic function h(x)=−6x2+384h(x) = -6x^2 + 384. To find the zeros, we set h(x)h(x) to zero and solve for xx.\newline0=−6x2+3840 = -6x^2 + 384
  2. Solve for zeros: Divide both sides of the equation by −6 -6 to simplify the equation.0=−6x2+3840 = -6x^2 + 3840=x2−640 = x^2 - 64
  3. Simplify the equation: Factor the quadratic equation.\newlineWe recognize that 6464 is a perfect square, so we can write the equation as:\newline0=(x−8)(x+8)0 = (x - 8)(x + 8)
  4. Factor the quadratic equation: Set each factor equal to zero and solve for xx.
    x−8=0x - 8 = 0 or x+8=0x + 8 = 0
    x=8x = 8 or x=−8x = -8

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