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

April 7, 2026Mathematics

ScanSolve AI Answer

April 7, 2026

Answer

x=1, x=2

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

Step 1: Identify the coefficients $a$ , $b$ , and $c$ from the equation $ax^2 + bx + c = 0$ . For $x^2 - 3x + 2 = 0$ : $a = 1$ $b = -3$ $c = 2$

Step 2: Substitute these values into the quadratic formula. $x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(2)}}{2(1)}$

Step 3: Simplify the expression under the square root and the denominator. $x = \frac{3 \pm \sqrt{9 - 8}}{2}$ $x = \frac{3 \pm \sqrt{1}}{2}$ $x = \frac{3 \pm 1}{2}$

Step 4: Calculate the two possible values for $x$ . For the first solution (using the + sign): $x_1 = \frac{3 + 1}{2} = \frac{4}{2} = 2$ For the second solution (using the - sign): $x_2 = \frac{3 - 1}{2} = \frac{2}{2} = 1$

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

The final answer is $\boxed{x=1, x=2}$ .

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Quick Answer

To solve the quadratic equation x^2 - 3x + 2 = 0 using the quadratic formula, we use the formula x = -b ± sqrt(b^2 - 4ac)2a.

Asked on April 7, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 7, 2026

To solve the quadratic equation x^2 - 3x + 2 = 0 using the quadratic formula, we use the formula x = -b ± sqrt(b^2 - 4ac)2a. Step 1: Identify the coefficients a, b, and c from the equation ax^2 + bx + c = 0. For x^2 - 3x + 2 = 0: a = 1 b = -3 c = 2 Step 2: Substitute these values into the quadratic formula. x = -(-3) ± sqrt((-3)^2 - 4(1)(2))2(1) Step 3: Simplify the expression under the square root and the denominator. x = 3 ± sqrt(9 - 8)2 x = 3 ± sqrt(1)2 x = (3 ± 1)/(2) Step 4: Calculate the two possible values for x. For the first solution (using the + sign): x_1 = (3 + 1)/(2) = (4)/(2) = 2 For the second solution (using the - sign): x_2 = (3 - 1)/(2) = (2)/(2) = 1 The solutions are x = 1 and x = 2. The final answer is x=1, x=2.