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Solve using the quadratic formula.\newline3k2+8k+5=03k^2 + 8k + 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____

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Q. Solve using the quadratic formula.\newline3k2+8k+5=03k^2 + 8k + 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 3k2+8k+5=03k^2 + 8k + 5 = 0.a=3a = 3, b=8b = 8, c=5c = 5.
  2. Write quadratic formula: Write down the quadratic formula: k=−b±b2−4ac2ak = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.k=−(8)±(8)2−4(3)(5)2(3).k = \frac{{-(8) \pm \sqrt{{(8)^2 - 4(3)(5)}}}}{{2(3)}}.
  4. Calculate discriminant: Calculate the discriminant (b2−4ac)(b^2 - 4ac). Discriminant = (8)2−4(3)(5)=64−60=4(8)^2 - 4(3)(5) = 64 - 60 = 4.
  5. Calculate square root: Calculate the square root of the discriminant.\newline4=2\sqrt{4} = 2.
  6. Substitute back into formula: Substitute the square root of the discriminant back into the quadratic formula.\newlinek=−8±26k = \frac{{-8 \pm 2}}{6}.
  7. Calculate possible solutions: Calculate the two possible solutions for kk.k=(−8+2)/6k = (-8 + 2) / 6 or k=(−8−2)/6k = (-8 - 2) / 6.k=−6/6k = -6 / 6 or k=−10/6k = -10 / 6.
  8. Simplify fractions: Simplify the fractions to get the solutions in simplest form. \newlinek=−1k = -1 or k=−106k = -\frac{10}{6}.\newlinek=−1k = -1 or k=−53k = -\frac{5}{3}.
  9. Round decimal solutions: If necessary, round the decimal solutions to the nearest hundredth. k=−1.00k = -1.00 or k=−1.67k = -1.67.

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