If b²-4ac = 0
1 real root
If the equation b²-4ac = 0, where a, b, and c are constants, it means that the quadratic equation ax² + bx + c = 0 has one real root or solution. This is because the expression b²-4ac is called the discriminant of the quadratic equation, which is used to determine the number and nature of the roots based on its value.
If the discriminant is zero, then the quadratic equation has only one real root, which is equal to – b/2a. This is because the quadratic formula for finding the roots of a quadratic equation is given by:
x = (-b ± √(b²-4ac)) / 2a
When the discriminant is zero, the square root term in the quadratic formula becomes zero, which means that one of the two roots of the equation is equal to – b/2a. The other root is also – b/2a since the sum of the roots is -b/a and their product is c/a.
Therefore, if b²-4ac = 0, the quadratic equation has exactly one real root, which is given by x = – b/2a.
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