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Solve using the quadratic formula.\newline3r2−5r+2=03r^2 - 5r + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____

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Q. Solve using the quadratic formula.\newline3r2−5r+2=03r^2 - 5r + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____
  1. Quadratic Formula: The quadratic formula is given by r=−b±b2−4ac2ar = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=3a = 3, b=−5b = -5, and c=2c = 2.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is (−5)2−4(3)(2)(-5)^2 - 4(3)(2).
  3. Perform Calculation: Perform the calculation: (−5)2−4(3)(2)=25−24=1(-5)^2 - 4(3)(2) = 25 - 24 = 1.
  4. Plug in Discriminant: Now, plug the discriminant back into the quadratic formula to find the two possible values for rr. The formula becomes r=−(−5)±12×3r = \frac{-(-5) \pm \sqrt{1}}{2 \times 3}.
  5. Simplify Formula: Simplify the formula: r=5±16r = \frac{5 \pm 1}{6}.
  6. Find Solutions: Find the two possible solutions for rr by performing the addition and subtraction: r=5+16r = \frac{5 + 1}{6} and r=5−16r = \frac{5 - 1}{6}.
  7. Calculate Solutions: Calculate the two solutions: r=66r = \frac{6}{6} and r=46r = \frac{4}{6}.
  8. Final Answers: Simplify the fractions to get the final answers: r=1r = 1 and r=23r = \frac{2}{3}.

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