If b²-4ac = 0
If the expression b²-4ac equals zero in the context of a quadratic equation, it means that the equation has exactly one real root or solution
If the expression b²-4ac equals zero in the context of a quadratic equation, it means that the equation has exactly one real root or solution. This condition is known as the discriminant being equal to zero.
In the quadratic equation form: ax² + bx + c = 0, the discriminant is represented by the expression b²-4ac.
If b²-4ac is equal to zero, it implies that the quadratic equation has a double root. In other words, the graph of the equation will have only one x-intercept or solution. This occurs when the parabola representing the equation just touches the x-axis.
To find the solution(s) for the quadratic equation when b²-4ac = 0, you can use the quadratic formula. The quadratic formula is given as:
x = (-b ± √(b²-4ac)) / (2a)
When the discriminant value is zero, we have:
x = (-b ± √0) / (2a)
Since the square root of 0 is 0, we can simplify the equation to:
x = -b / (2a)
Therefore, for a quadratic equation where b²-4ac = 0, the solution will be a single real root given by -b / (2a).
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