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Solve the quadratic equation x2 − 3x + 2 = 0 using the quadratic formula.

Mathematics

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Answer

x=1,x=2x=1, x=2

Step-by-step solution

4 steps

To solve the quadratic equation x2−3x+2=0x^2 - 3x + 2 = 0 using the quadratic formula, we use the formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

  1. Identify the coefficients aa, bb, and cc from the equation ax2+bx+c=0ax^2 + bx + c = 0.

    For x2−3x+2=0x^2 - 3x + 2 = 0:
    a=1a = 1
    b=−3b = -3
    c=2c = 2

  2. Substitute these values into the quadratic formula.

    x=−(−3)±(−3)2−4(1)(2)2(1)x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(2)}}{2(1)}

  3. Simplify the expression under the square root and the denominator.

    x=3±9−82x = \frac{3 \pm \sqrt{9 - 8}}{2} x=3±12x = \frac{3 \pm \sqrt{1}}{2} x=3±12x = \frac{3 \pm 1}{2}

  4. Calculate the two possible values for xx.

    For the first solution (using the + sign):

    x1=3+12=42=2x_1 = \frac{3 + 1}{2} = \frac{4}{2} = 2

    For the second solution (using the - sign):

    x2=3−12=22=1x_2 = \frac{3 - 1}{2} = \frac{2}{2} = 1

    The solutions are x=1x = 1 and x=2x = 2.

    The final answer is x=1,x=2x=1, x=2.

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