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Find the zeros of the function f(x)=x^(2)+3.8 x-1.8. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=x2+3.8x−1.8 f(x)=x^{2}+3.8 x-1.8 . 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+3.8x−1.8 f(x)=x^{2}+3.8 x-1.8 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Identify Equation Type: Identify the type of equation and the method to find its zeros.\newlineThe given function is a quadratic equation of the form f(x)=ax2+bx+cf(x) = ax^2 + bx + c. To find the zeros of the function, we need to solve the equation x2+3.8x−1.8=0x^2 + 3.8x - 1.8 = 0. We can use the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=1a = 1, b=3.8b = 3.8, and c=−1.8c = -1.8.
  2. Apply Quadratic Formula: Apply the quadratic formula to find the zeros of the function.\newlineUsing the quadratic formula, we have:\newlinex=−3.8±3.82−4(1)(−1.8)2(1)x = \frac{-3.8 \pm \sqrt{3.8^2 - 4(1)(-1.8)}}{2(1)}\newlinex=−3.8±14.44+7.22x = \frac{-3.8 \pm \sqrt{14.44 + 7.2}}{2}\newlinex=−3.8±21.642x = \frac{-3.8 \pm \sqrt{21.64}}{2}
  3. Calculate Discriminant and Zeros: Calculate the discriminant and the zeros.\newlineFirst, calculate the square root of the discriminant:\newline21.64≈4.65\sqrt{21.64} \approx 4.65\newlineNow, calculate the two possible values for xx:\newlinex=(−3.8+4.652)x = (\frac{-3.8 + 4.65}{2}) and x=(−3.8−4.652)x = (\frac{-3.8 - 4.65}{2})\newlinex≈0.425x \approx 0.425 and x≈−4.225x \approx -4.225
  4. Round Zeros: Round the zeros to the nearest hundredth.\newlineRounding the values to the nearest hundredth, we get:\newlinex≈0.43x \approx 0.43 and x≈−4.23x \approx -4.23

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