Find the zeros of the function $f(x)=2 x^{2}-18 x+35.4$ . Round values to the nearest hundredth (if necessary). $\newline$ Answer: $x=$

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Q. Find the zeros of the function

f(x)=2 x^{2}-18 x+35.4

. Round values to the nearest hundredth (if necessary).

\newline

Answer:

x=

Quadratic Formula: To find the zeros of the function $f(x) = 2x^2 - 18x + 35.4$ , we need to solve the quadratic equation $2x^2 - 18x + 35.4 = 0$ . We can use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 2$ , $b = -18$ , and $c = 35.4$ .
Calculate Discriminant: First, calculate the discriminant, which is $b^2 - 4ac$ . Here, $b = -18$ , $a = 2$ , and $c = 35.4$ . So, the discriminant is $(-18)^2 - 4 \times 2 \times 35.4$ .
Apply Quadratic Formula: Calculating the discriminant: $(-18)^2 - 4 \times 2 \times 35.4 = 324 - 8 \times 35.4 = 324 - 283.2 = 40.8$ .
Calculate Square Root: Now, we can apply the quadratic formula. The two solutions for $x$ will be: $\newline$ $x = \frac{-(-18) \pm \sqrt{40.8}}{(2 \times 2)}$ $\newline$ $x = \frac{18 \pm \sqrt{40.8}}{4}$
Find Zeros: Calculate the square root of the discriminant: $\sqrt{40.8} \approx 6.39$ (rounded to two decimal places).
Find Zeros: Calculate the square root of the discriminant: $\sqrt{40.8} \approx 6.39$ (rounded to two decimal places).Now, plug the value of the square root back into the formula to find the two zeros: $\newline$ $x = \frac{18 + 6.39}{4}$ and $x = \frac{18 - 6.39}{4}$
Find Zeros: Calculate the square root of the discriminant: $\sqrt{40.8} \approx 6.39$ (rounded to two decimal places).Now, plug the value of the square root back into the formula to find the two zeros: $\newline$ $x = \frac{18 + 6.39}{4}$ and $x = \frac{18 - 6.39}{4}$ Calculate the two values for x: $\newline$ $x \approx \frac{18 + 6.39}{4} \approx \frac{24.39}{4} \approx 6.10$ (rounded to the nearest hundredth) $\newline$ $x \approx \frac{18 - 6.39}{4} \approx \frac{11.61}{4} \approx 2.90$ (rounded to the nearest hundredth)