Understanding Quadratic Equations: Finding Two Real and Distinct Roots Using Discriminant

If b²-4ac > 0

There are 2 real roots

If b²-4ac > 0, this means that the quadratic equation ax² + bx + c = 0 has two real and distinct roots. In this case, the discriminant (b²-4ac) is a positive number, which means that the square root of the discriminant is a real number. This allows us to use the quadratic formula to find the values of x that satisfy the equation:

x = (-b ± √(b²-4ac)) / 2a

The two values of x obtained by using the quadratic formula are the two real and distinct roots. The graph of the quadratic equation will intersect the x-axis at two points.

For example, if we have the quadratic equation x² + 4x + 3 = 0, we can use the quadratic formula to find the values of x:

x = (-4 ± √(4²-4(1)(3))) / 2(1)
x = (-4 ± √4) / 2
x1 = -3 and x2 = -1

Therefore, the quadratic equation x² + 4x + 3 = 0 has two real and distinct roots: x1 = -3 and x2 = -1.

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