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Find the zeros of the function f(x)=x^(2)-7.6 x+7.2. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=x2−7.6x+7.2 f(x)=x^{2}-7.6 x+7.2 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=x2−7.6x+7.2 f(x)=x^{2}-7.6 x+7.2 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Identify type of equation: Identify the type of equation.\newlineWe have a quadratic equation in the form f(x)=ax2+bx+cf(x) = ax^2 + bx + c, where a=1a = 1, b=−7.6b = -7.6, and c=7.2c = 7.2.
  2. Use quadratic formula: Use the quadratic formula to find the zeros of the function.\newlineThe quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. For our equation, a=1a = 1, b=−7.6b = -7.6, and c=7.2c = 7.2.
  3. Calculate discriminant: Calculate the discriminant b2−4acb^2 - 4ac.\newlineDiscriminant = (−7.6)2−4(1)(7.2)=57.76−28.8=28.96(-7.6)^2 - 4(1)(7.2) = 57.76 - 28.8 = 28.96.
  4. Calculate two possible values: Calculate the two possible values for xx using the quadratic formula.\newlinex=−(−7.6)±28.96(2⋅1)x = \frac{-(-7.6) \pm \sqrt{28.96}}{(2 \cdot 1)}\newlinex=7.6±28.962x = \frac{7.6 \pm \sqrt{28.96}}{2}
  5. Find square root: Find the square root of the discriminant. 28.96≈5.38\sqrt{28.96} \approx 5.38
  6. Calculate two solutions: Calculate the two solutions for xx.x1=7.6+5.382≈6.49x_1 = \frac{7.6 + 5.38}{2} \approx 6.49x2=7.6−5.382≈1.11x_2 = \frac{7.6 - 5.38}{2} \approx 1.11
  7. Round solutions: Round the solutions to the nearest hundredth.\newlinex1≈6.49x_1 \approx 6.49 (rounded to the nearest hundredth)\newlinex2≈1.11x_2 \approx 1.11 (rounded to the nearest hundredth)

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