Discover How To Find Repeated Roots In Quadratic Equations With B²-4Ac = 0

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.

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