Find the roots of the quadratic equation: 3x2 - 5x + 2 = 0 using the quadratic formula.
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Step-by-Step Solution
Step 1: Identify coefficients
First, we compare the given quadratic equation 3x2−5x+2=0 with the standard form of a quadratic equation, ax2+bx+c=0. This allows us to identify the coefficients a, b, and c.
Step 2: Apply the quadratic formula
Next, we write down the quadratic formula, which is used to find the roots of any quadratic equation. This formula provides a direct way to calculate the values of x.
Step 3: Substitute values into the formula
Now, we substitute the identified values of a=3, b=−5, and c=2 into the quadratic formula. This is the crucial step before performing the calculations.
Step 4: Simplify the expression
We simplify the expression under the square root and perform the multiplication in the denominator. The term b2−4ac is called the discriminant, and its value helps determine the nature of the roots.
Step 5: Calculate the roots
Finally, we calculate the two possible roots by considering both the positive and negative signs of the square root. This gives us the two solutions for x.