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Find the zeros of the function f(x)=x^(2)-6.9 x+4. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=x2−6.9x+4 f(x)=x^{2}-6.9 x+4 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Full solution

Q. Find the zeros of the function f(x)=x2−6.9x+4 f(x)=x^{2}-6.9 x+4 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Recognize quadratic function: Recognize that the function f(x)=x2−6.9x+4f(x) = x^2 - 6.9x + 4 is a quadratic equation, and the zeros of the function can be found by setting f(x)f(x) to zero and solving for xx.
  2. Set equation to zero: Set the quadratic equation to zero: 0=x2−6.9x+40 = x^2 - 6.9x + 4.
  3. Use quadratic formula: Use the quadratic formula to solve for xx, where a=1a = 1, b=−6.9b = -6.9, and c=4c = 4. The quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  4. Calculate discriminant: Calculate the discriminant, which is the part under the square root in the quadratic formula: discriminant=b2−4ac=(−6.9)2−4(1)(4)\text{discriminant} = b^2 - 4ac = (-6.9)^2 - 4(1)(4).
  5. Perform calculation: Perform the calculation: discriminant=47.61−16=31.61\text{discriminant} = 47.61 - 16 = 31.61.
  6. Insert values into formula: Insert the values into the quadratic formula: x=6.9±31.612x = \frac{6.9 \pm \sqrt{31.61}}{2}.
  7. Calculate possible values: Calculate the two possible values for xx: x1=6.9+31.612x_1 = \frac{6.9 + \sqrt{31.61}}{2} and x2=6.9−31.612x_2 = \frac{6.9 - \sqrt{31.61}}{2}.
  8. Round to nearest hundredth: Calculate the numerical values and round to the nearest hundredth: x1≈(6.9+5.62)/2≈6.26x_1 \approx (6.9 + 5.62) / 2 \approx 6.26 and x2≈(6.9−5.62)/2≈0.64x_2 \approx (6.9 - 5.62) / 2 \approx 0.64.

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