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Find the zeros of the function f(x)=2x^(2)+7.3 x-1. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=2x2+7.3x−1 f(x)=2 x^{2}+7.3 x-1 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=2x2+7.3x−1 f(x)=2 x^{2}+7.3 x-1 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Set up quadratic equation: Set up the quadratic equation to find the zeros.\newlineTo find the zeros of the function f(x)=2x2+7.3x−1f(x) = 2x^2 + 7.3x - 1, we need to solve the equation 2x2+7.3x−1=02x^2 + 7.3x - 1 = 0.
  2. Use quadratic formula: Use the quadratic formula to solve for xx. The quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=2a = 2, b=7.3b = 7.3, and c=−1c = -1.
  3. Calculate discriminant: Calculate the discriminant.\newlineThe discriminant is the part of the quadratic formula under the square root: b2−4acb^2 - 4ac. Let's calculate it:\newlineDiscriminant = (7.3)2−4×2×(−1)=53.29+8=61.29(7.3)^2 - 4 \times 2 \times (-1) = 53.29 + 8 = 61.29.
  4. Calculate possible values for x: Calculate the two possible values for x using the quadratic formula.\newlinex=−7.3±61.292×2x = \frac{-7.3 \pm \sqrt{61.29}}{2 \times 2}\newlinex=−7.3±7.8270714x = \frac{-7.3 \pm 7.827071}{4}
  5. Calculate zeros: Calculate the two zeros by solving for xx.\newlineFirst zero:\newlinex=−7.3+7.8270714x = \frac{-7.3 + 7.827071}{4}\newlinex=0.5270714x = \frac{0.527071}{4}\newlinex≈0.13x \approx 0.13\newlineSecond zero:\newlinex=−7.3−7.8270714x = \frac{-7.3 - 7.827071}{4}\newlinex=−15.1270714x = \frac{-15.127071}{4}\newlinex≈−3.78x \approx -3.78

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