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Find the real zeros of the quadratic function using any method you wish. What are the x-intercepts, if any, of the graph of the function?

f(x)=x^(2)-50

Find the real zeros of the quadratic function using any method you wish. What are the x-intercepts, if any, of the graph of the function?\newlinef(x)=x250 f(x)=x^{2}-50

Full solution

Q. Find the real zeros of the quadratic function using any method you wish. What are the x-intercepts, if any, of the graph of the function?\newlinef(x)=x250 f(x)=x^{2}-50
  1. Set equation to zero: To find the real zeros of the quadratic function f(x)=x250f(x) = x^2 - 50, we need to set the function equal to zero and solve for xx.0=x2500 = x^2 - 50
  2. Solve for xx: We can solve this equation by taking the square root of both sides. However, since we are taking the square root of a negative number, we will have two solutions, one positive and one negative.\newlinex2=50x^2 = 50
  3. Square root both sides: Taking the square root of both sides gives us:\newlinex=±50x = \pm\sqrt{50}
  4. Simplify square root: Simplifying the square root of 5050, we get:\newlinex=±25×2x = \pm\sqrt{25 \times 2}\newlinex=±52x = \pm5\sqrt{2}
  5. Identify real zeros: Therefore, the real zeros of the function are x=52x = 5\sqrt{2} and x=52x = -5\sqrt{2}. These zeros are also the xx-intercepts of the graph of the function.

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