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Solve using the quadratic formula.\newline4k2−7k+3=04k^2 - 7k + 3 = 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.\newline4k2−7k+3=04k^2 - 7k + 3 = 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 4k2−7k+3=04k^2 - 7k + 3 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.a=4a = 4, b=−7b = -7, c=3c = 3
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula, k=−b±b2−4ac2ak = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
    k=−(−7)±(−7)2−4⋅4⋅32⋅4k = \frac{-(-7) \pm \sqrt{(-7)^2 - 4\cdot4\cdot3}}{2\cdot4}
  3. Simplify expression: Simplify the expression inside the square root and the constants outside the square root.\newlinek=7±49−488k = \frac{7 \pm \sqrt{49 - 48}}{8}\newlinek=7±18k = \frac{7 \pm \sqrt{1}}{8}
  4. Calculate possible solutions: Calculate the two possible solutions for kk using the simplified square root.k=7+18k = \frac{7 + 1}{8} or k=7−18k = \frac{7 - 1}{8}k=88k = \frac{8}{8} or k=68k = \frac{6}{8}
  5. Simplify fractions: Simplify the fractions to get the final solutions for kk.k=1k = 1 or k=68k = \frac{6}{8}k=1k = 1 or k=34k = \frac{3}{4}
  6. Round non-integer solution: If necessary, round the non-integer solution to the nearest hundredth. k=1k = 1 or k=0.75k = 0.75 (since 34\frac{3}{4} is already in simplest form and does not need rounding)

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