Solve the quadratic equation x2 - 5x + 6 = 0
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Step-by-Step Solution
Step 1: Identify coefficients
A quadratic equation is generally written in the form ax2+bx+c=0. We need to identify the values of a, b, and c from the given equation.
Step 2: Apply the quadratic formula
The quadratic formula is used to find the solutions (roots) of any quadratic equation. We will substitute the values of a, b, and c into this formula.
Step 3: Substitute values into the formula
Substitute a=1, b=−5, and c=6 into the quadratic formula. This will allow us to calculate the values of x.
Step 4: Simplify the expression
Simplify the expression under the square root and perform the multiplication in the denominator. This step brings us closer to finding the roots.
Step 5: Calculate the roots
Now, we calculate the two possible values for x by considering both the positive and negative square roots. These are the two roots of the quadratic equation.