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Find the zeros of the function f(x)=x^(2)+5.4 x+4. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=x2+5.4x+4 f(x)=x^{2}+5.4 x+4 . 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+5.4x+4 f(x)=x^{2}+5.4 x+4 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Calculate Discriminant: To find the zeros of the function f(x)=x2+5.4x+4f(x) = x^2 + 5.4x + 4, we need to solve the quadratic equation x2+5.4x+4=0x^2 + 5.4x + 4 = 0. We can use the quadratic formula, which is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=1a = 1, b=5.4b = 5.4, and c=4c = 4.
  2. Find Square Root: First, we calculate the discriminant, which is b2−4acb^2 - 4ac. Plugging in the values, we get (5.4)2−4(1)(4)=29.16−16=13.16(5.4)^2 - 4(1)(4) = 29.16 - 16 = 13.16.
  3. Apply Quadratic Formula: Now, we take the square root of the discriminant: 13.16≈3.63\sqrt{13.16} \approx 3.63.
  4. Calculate Positive Solution: Next, we apply the quadratic formula. The two possible solutions for xx are:\newlinex=−5.4±3.632×1x = \frac{{-5.4 \pm 3.63}}{{2 \times 1}}
  5. Calculate Negative Solution: We calculate the two solutions separately:\newlineFor the positive square root: x=−5.4+3.632≈−0.885x = \frac{{-5.4 + 3.63}}{{2}} \approx -0.885\newlineFor the negative square root: x=−5.4−3.632≈−4.515x = \frac{{-5.4 - 3.63}}{{2}} \approx -4.515
  6. Round Solutions: We round both solutions to the nearest hundredth:\newlinex≈−0.89x \approx -0.89 (for the positive square root)\newlinex≈−4.52x \approx -4.52 (for the negative square root)

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