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Find the zeros of the following quadratic function using the square root method. What are the x-intercepts of the graph of the function? f(x)=x^(2)-50

Find the zeros of the following quadratic function using the square root method. What are the x-intercepts of the graph of the function?\newlinef(x)=x2−50 f(x)=x^{2}-50

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Quadratic equation with complex rootsright chevron icon

Full solution

Q. Find the zeros of the following quadratic function using the square root method. What are the x-intercepts of the graph of the function?\newlinef(x)=x2−50 f(x)=x^{2}-50
  1. Set Function Equal: Set the function equal to zero to find the x-intercepts. f(x)=x2−50=0f(x) = x^2 - 50 = 0
  2. Square Root Method: Apply the square root method to solve for xx.x2=50x^2 = 50Take the square root of both sides of the equation.x=±50x = \pm\sqrt{50}
  3. Simplify Square Root: Simplify the square root. 50\sqrt{50} can be simplified to (25×2)\sqrt{(25\times2)} which is 525\sqrt{2}. x=±52x = \pm5\sqrt{2}
  4. Write Final Answer: Write the final answer in simplest form.\newlineThe x-intercepts of the graph of the function are x=52x = 5\sqrt{2} and x=−52x = -5\sqrt{2}.

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