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Find the zeros of the function f(x)=1.1x^(2)-2.5 x-1. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=1.1x2−2.5x−1 f(x)=1.1 x^{2}-2.5 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)=1.1x2−2.5x−1 f(x)=1.1 x^{2}-2.5 x-1 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Set Function Equal to Zero: Set the function equal to zero to find its zeros.\newlinef(x)=1.1x2−2.5x−1=0f(x) = 1.1x^2 - 2.5x - 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 a=1.1a = 1.1, b=−2.5b = -2.5, and c=−1c = -1.
  3. Calculate Discriminant: Calculate the discriminant, which is b2−4acb^2 - 4ac.\newlineDiscriminant = (−2.5)2−4(1.1)(−1)=6.25+4.4=10.65(-2.5)^2 - 4(1.1)(-1) = 6.25 + 4.4 = 10.65
  4. Calculate Two Solutions: Since the discriminant is positive, there will be two real solutions. Calculate the two solutions using the quadratic formula.\newlinex=−(−2.5)±10.652×1.1x = \frac{-(-2.5) \pm \sqrt{10.65}}{2 \times 1.1}
  5. Calculate Positive Square Root: Calculate the positive square root of the discriminant.\newline10.65≈3.26\sqrt{10.65} \approx 3.26 (rounded to two decimal places)
  6. Calculate Values of x: Calculate the two values of x.\newlinex1=2.5+3.262×1.1≈2.62x_1 = \frac{2.5 + 3.26}{2 \times 1.1} \approx 2.62\newlinex2=2.5−3.262×1.1≈−0.35x_2 = \frac{2.5 - 3.26}{2 \times 1.1} \approx -0.35

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