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Find the zeros of the function f(x)=2x^(2)-13.1 x+18. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=2x2−13.1x+18 f(x)=2 x^{2}-13.1 x+18 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=2x2−13.1x+18 f(x)=2 x^{2}-13.1 x+18 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Calculate Discriminant: To find the zeros of the function f(x)=2x2−13.1x+18f(x) = 2x^2 - 13.1x + 18, we need to solve the quadratic equation 2x2−13.1x+18=02x^2 - 13.1x + 18 = 0. We can use the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=2a = 2, b=−13.1b = -13.1, and c=18c = 18.
  2. Apply Quadratic Formula: First, calculate the discriminant, which is b2−4acb^2 - 4ac. Here, b=−13.1b = -13.1, a=2a = 2, and c=18c = 18. So, the discriminant is (−13.1)2−4×2×18(-13.1)^2 - 4 \times 2 \times 18.
  3. Calculate Solutions: Calculating the discriminant gives us 171.61−144=27.61171.61 - 144 = 27.61.
  4. Calculate Square Root: Now, we can apply the quadratic formula. The two solutions for xx will be:\newlinex=−(−13.1)±27.612×2x = \frac{{-(-13.1) \pm \sqrt{27.61}}}{{2 \times 2}}\newlinex=13.1±27.614x = \frac{{13.1 \pm \sqrt{27.61}}}{4}
  5. Find Final Solutions: Calculating the square root of the discriminant, we get 27.61=5.26\sqrt{27.61} = 5.26.
  6. Round to Nearest Hundredth: Now we have two possible solutions for xx:x=13.1+5.264x = \frac{{13.1 + 5.26}}{{4}} and x=13.1−5.264x = \frac{{13.1 - 5.26}}{{4}}
  7. Round to Nearest Hundredth: Now we have two possible solutions for xx:x=13.1+5.264x = \frac{13.1 + 5.26}{4} and x=13.1−5.264x = \frac{13.1 - 5.26}{4}Calculating these, we get:x=18.364x = \frac{18.36}{4} and x=7.844x = \frac{7.84}{4}x=4.59x = 4.59 and x=1.96x = 1.96
  8. Round to Nearest Hundredth: Now we have two possible solutions for xx:x=13.1+5.264x = \frac{13.1 + 5.26}{4} and x=13.1−5.264x = \frac{13.1 - 5.26}{4}Calculating these, we get:x=18.364x = \frac{18.36}{4} and x=7.844x = \frac{7.84}{4}x=4.59x = 4.59 and x=1.96x = 1.96Rounding these values to the nearest hundredth, we get:x≈4.59x \approx 4.59 and x≈1.96x \approx 1.96

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