If b²-4ac = 0
1 real root
If the expression b²-4ac equals zero, then the quadratic equation ax²+bx+c=0 has one real root.
To explain why this is the case, we can start by using the quadratic formula, which is:
x = (-b ± √(b²-4ac))/2a
Here, the expression inside the square root is the discriminant, which determines the nature of the roots of the quadratic equation. If the discriminant is greater than zero, then the equation has two distinct real roots. If it is less than zero, then the equation has two complex roots. But if it is equal to zero, then the equation has only one real root.
So, if we substitute b²-4ac=0 into the quadratic formula, we get:
x = (-b ± √(0))/2a
Simplifying this further, we get:
x = (-b)/2a
Therefore, the quadratic equation ax²+bx+c=0 has only one real root, which is equal to (-b)/2a when b²-4ac=0.
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