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Find the zeros of the function f(x)=2x^(2)+10.1 x+5.3. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=2x2+10.1x+5.3 f(x)=2 x^{2}+10.1 x+5.3 . 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+10.1x+5.3 f(x)=2 x^{2}+10.1 x+5.3 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Identify equation type: Identify the type of the 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 can use the quadratic formula, which is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  2. Apply quadratic formula: Apply the quadratic formula to the given function.\newlineFor the function f(x)=2x2+10.1x+5.3f(x) = 2x^2 + 10.1x + 5.3, the coefficients are a=2a = 2, b=10.1b = 10.1, and c=5.3c = 5.3. Plugging these values into the quadratic formula gives us:\newlinex=−10.1±(10.1)2−4⋅2⋅5.32⋅2x = \frac{-10.1 \pm \sqrt{(10.1)^2 - 4 \cdot 2 \cdot 5.3}}{2 \cdot 2}
  3. Calculate discriminant: Calculate the discriminant (the part under the square root in the quadratic formula).\newlineThe discriminant is b2−4acb^2 - 4ac, so we calculate:\newline(10.1)2−4⋅2⋅5.3=102.01−42.4=59.61(10.1)^2 - 4\cdot2\cdot5.3 = 102.01 - 42.4 = 59.61
  4. Calculate x values: Calculate the two possible values for x using the quadratic formula.\newlineNow we have:\newlinex=−10.1±59.614x = \frac{-10.1 \pm \sqrt{59.61}}{4}\newlineWe will calculate both the positive and negative square root cases separately.
  5. Calculate x (positive): Calculate the value for x using the positive square root.\newlinex=−10.1+59.614x = \frac{{-10.1 + \sqrt{59.61}}}{{4}}\newlinex=−10.1+7.7254x = \frac{{-10.1 + 7.725}}{{4}}\newlinex=−2.3754x = \frac{{-2.375}}{{4}}\newlinex≈−0.59x \approx -0.59 (rounded to the nearest hundredth)
  6. Calculate xx (negative): Calculate the value for xx using the negative square root.\newlinex=−10.1−59.614x = \frac{{-10.1 - \sqrt{59.61}}}{{4}}\newlinex=−10.1−7.7254x = \frac{{-10.1 - 7.725}}{{4}}\newlinex=−17.8254x = \frac{{-17.825}}{{4}}\newlinex≈−4.46x \approx -4.46 (rounded to the nearest hundredth)

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