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Solve using the quadratic formula.\newline4m2−5m+1=04m^2 - 5m + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinem=m = _____ or m=m = _____

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Q. Solve using the quadratic formula.\newline4m2−5m+1=04m^2 - 5m + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinem=m = _____ or m=m = _____
  1. Quadratic Formula: The quadratic formula is given by m=−b±b2−4ac2am = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the terms in the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. For the equation 4m2−5m+1=04m^2 - 5m + 1 = 0, a=4a = 4, b=−5b = -5, and c=1c = 1.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. For our equation, the discriminant is (−5)2−4(4)(1)=25−16=9(-5)^2 - 4(4)(1) = 25 - 16 = 9.
  3. Apply Quadratic Formula: Now, apply the quadratic formula with the values of aa, bb, and cc to find the two possible values for mm.m=−(−5)±92×4m = \frac{-(-5) \pm \sqrt{9}}{2 \times 4}m=5±98m = \frac{5 \pm \sqrt{9}}{8}
  4. Find Solutions: Since the square root of 99 is 33, we can simplify the expression to find the two solutions for mm.
    m=5+38m = \frac{5 + 3}{8} or m=5−38m = \frac{5 - 3}{8}
    m=88m = \frac{8}{8} or m=28m = \frac{2}{8}
  5. Simplify Fractions: Simplify the fractions to get the final solutions for mm.m=1m = 1 or m=14m = \frac{1}{4}

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