A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. Here is an example of how to solve a quadratic equation:
Let's solve the quadratic equation x² + 2x - 3 = 0
Step 1: Identify the values of a, b, and c
Here, a = 1, b = 2, and c = -3
Step 2: Find the discriminant (b² - 4ac)
The discriminant is b² - 4ac = 2² - 4(1)(-3) = 16
Step 3: Use the discriminant to determine the nature of the roots
If the discriminant is positive, then there are two real roots.
If the discriminant is zero, then there is one real root.
If the discriminant is negative, then there are no real roots.
In this case, since the discriminant is positive, we know that there are two real roots.
Step 4: Solve for x using the quadratic formula, which is:
x = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a, b, and c, we get:
x = (-2 ± √(2² - 4(1)(-3))) / 2(1)
x = (-2 ± √16) / 2
x = (-2 ± 4) / 2
This gives us two possible solutions:
x = (-2+4)/2 = 1
x = (-2-4)/2 = -3
So the roots of the quadratic equation x² + 2x - 3 = 0 are x = 1 and x = -3.
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