If b²-4ac = 0
1 real root
If b²-4ac = 0, then the quadratic equation ax²+bx+c=0 has only one real root. This root will be a repeated root, also called a double root or root of multiplicity 2.
We can find this root by using the quadratic formula: x = (-b ± √(b²-4ac))/2a. When b²-4ac = 0, the denominator of the quadratic formula becomes 2a*0 = 0 and we cannot divide by zero. However, we can use some algebraic manipulation to find the repeated root:
b²-4ac = 0
b² = 4ac
b = ±2√ac
Now we can substitute this value of b into the quadratic formula:
x = (-b ± √(b²-4ac))/2a
x = (-±2√ac ± √(4ac))/2a
x = (-±2√ac ± 2√ac)/2a
x = -b/2a
So the repeated root is -b/2a. This means that the quadratic equation has only one solution, which is equal to -b/2a.
Note that when b²-4ac > 0, the quadratic equation has two distinct real roots, and when b²-4ac < 0, the quadratic equation has two complex conjugate roots.
More Answers:
[next_post_link]