First, we compare the given quadratic equation 2x² - 7x + 3 = 0 with the standard form ax² + bx + c = 0 to identify the coefficients a, b, and c. Then, we recall the quadratic formula, which provides the roots of the equation.

First, we compare the given quadratic equation 2x² - 7x + 3 = 0 with the standard form ax² + bx + c = 0 to identify the coefficients a, b, and c. Then, we recall the quadratic formula, which provides the roots of the equation.

Find the roots of the quadratic equation $2x^2 - 7x + 3 = 0$ using the quadratic formula, and state the value of the discriminant.

Answer: The roots of the quadratic equation are $x = 3$ and $x = \frac{1}{2}$ . The discriminant is $25$ .

Step-by-step solution

Step 1: Identify coefficients and the quadratic formula

First, we compare the given quadratic equation $2x^2 - 7x + 3 = 0$ with the standard form $ax^2 + bx + c = 0$ to identify the coefficients $a$ , $b$ , and $c$ . Then, we recall the quadratic formula, which provides the roots of the equation.

Step 2: Calculate the discriminant

The discriminant, $D = b^2 - 4ac$ , determines the nature of the roots. We substitute the values of $a$ , $b$ , and $c$ into this formula to calculate its value.

Step 3: Substitute values into the quadratic formula

Now that we have the discriminant, we substitute the values of $a$ , $b$ , and $D$ into the quadratic formula. This will allow us to find the two roots of the equation.

Step 4: Simplify and find the roots

We simplify the expression by calculating the square root of the discriminant and then performing the addition and subtraction operations to find the two distinct roots.

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Find the roots of the quadratic equation 2x2−7x+3=02x^2 - 7x + 3 = 02x2−7x+3=0 using the quadratic formula, and state the value of the discriminant.