Find the roots of the quadratic equation 2x2 - 7x + 3 = 0 using the quadratic formula, and state the value of the discriminant.
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Step-by-Step Solution
Step 1: Identify coefficients and the quadratic formula
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.
Step 2: Calculate the discriminant
The discriminant, D=b2−4ac, 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.