quadratic formula
x = -b ± √(b² – 4ac)/2a
The quadratic formula is a general formula used to solve any quadratic equation, which can be written in the form of:
ax^2 + bx + c = 0, where a, b, and c are coefficients, and x is the variable.
The quadratic formula is:
x = (-b ± √(b^2 – 4ac)) / 2a
where ± indicates that there are two possible solutions, the positive and negative values.
To use the quadratic formula, we simply substitute the values of a, b, and c into the formula, compute the values of the positive and negative solutions, and verify that they satisfy the original equation.
For example, let’s solve the quadratic equation: 2x^2 + 5x – 3 = 0
In this case, a = 2, b = 5, and c = -3. Substituting these values into the quadratic formula, we get:
x = (-5 ± √(5^2 – 4(2)(-3))) / 2(2)
x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √49) / 4
So, the two possible solutions are:
x = (-5 + 7) / 4 = 1/2
x = (-5 – 7) / 4 = -3
Therefore, the solutions of the quadratic equation 2x^2 + 5x – 3 = 0 are x = 1/2 and x = -3. We can verify that these solutions satisfy the equation by substituting them back into the original equation and observing that both sides of the equation are equal.
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