First, we compare the given quadratic equation 3x² - 5x + 2 = 0 with the standard form of a quadratic equation, ax² + bx + c = 0. By comparing the coefficients, we identify the values for a, b, and c.

First, we compare the given quadratic equation 3x² - 5x + 2 = 0 with the standard form of a quadratic equation, ax² + bx + c = 0. By comparing the coefficients, we identify the values for a, b, and c.

Now, we substitute the identified values of a=3, b=-5, and c=2 into the quadratic formula x = (-b ± √(b² - 4ac))/(2a). This sets up the equation for solving x.

We simplify the expression under the square root, which is the discriminant. First, we calculate (-5)² = 25 and 4(3)(2) = 24. Then, we subtract these values to get 25 - 24 = 1.

The square root of 1 is 1. We replace √1 with 1 in the formula.

Finally, we calculate the two possible values for x. For the first value, we use the plus sign: x_1 = (5 + 1)/(6) = (6)/(6) = 1. For the second value, we use the minus sign: x_2 = (5 - 1)/(6) = (4)/(6) = (2)/(3).

Finally, we calculate the two possible values for x. For the first value, we use the plus sign: x_1 = (5 + 1)/(6) = (6)/(6) = 1. For the second value, we use the minus sign: x_2 = (5 - 1)/(6) = (4)/(6) = (2)/(3).

Solve the quadratic equation $3x^2 - 5x + 2 = 0$ using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .

Answer: The solutions to the quadratic equation $3x^2 - 5x + 2 = 0$ are $x = 1$ and $x = \frac{2}{3}$ .

Step-by-step solution

Step 1: Identify coefficients

First, we compare the given quadratic equation $3x^2 - 5x + 2 = 0$ with the standard form of a quadratic equation, $ax^2 + bx + c = 0$ . By comparing the coefficients, we identify the values for $a$ , $b$ , and $c$ .

Step 2: Substitute into the quadratic formula

Now, we substitute the identified values of $a=3$ , $b=-5$ , and $c=2$ into the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . This sets up the equation for solving $x$ .

Step 3: Simplify the expression under the square root

We simplify the expression under the square root, which is the discriminant. First, we calculate $(-5)^2 = 25$ and $4(3)(2) = 24$ . Then, we subtract these values to get $25 - 24 = 1$ .

Step 4: Calculate the square root

The square root of $1$ is $1$ . We replace $\sqrt{1}$ with $1$ in the formula.

Step 5: Find the two possible values for x

Finally, we calculate the two possible values for $x$ . For the first value, we use the plus sign: $x_1 = \frac{5 + 1}{6} = \frac{6}{6} = 1$ . For the second value, we use the minus sign: $x_2 = \frac{5 - 1}{6} = \frac{4}{6} = \frac{2}{3}$ .

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Solve the quadratic equation 3x2−5x+2=03x^2 - 5x + 2 = 03x2−5x+2=0 using the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​.