Explaining the Condition for Two Distinct Real Solutions in Quadratic Equations

If b²-4ac > 0

If b²-4ac > 0, then the quadratic equation ax² + bx + c = 0 will have two distinct real solutions

If b²-4ac > 0, then the quadratic equation ax² + bx + c = 0 will have two distinct real solutions.

The quadratic formula can be used to find the solutions of a quadratic equation. It is given by:

x = (-b ± √(b²-4ac)) / (2a)

In this case, if b²-4ac > 0, it means that the discriminant (b²-4ac) is positive. The discriminant determines the nature of the solutions.

When the discriminant is positive, it indicates that there are two distinct real solutions. These solutions will be found by taking the square root of the positive discriminant.

Let’s go through an example to demonstrate this:

Suppose we have the quadratic equation 2x² + 3x – 5 = 0.

In this case, a = 2, b = 3, and c = -5.

We can calculate the discriminant as follows:

b²-4ac = (3)² – 4(2)(-5)
= 9 + 40
= 49

Since the discriminant is positive (49 > 0), we can apply the quadratic formula:

x = (-3 ± √(49)) / (2*2)
= (-3 ± 7) / 4

This gives us two solutions:

x₁ = (-3 + 7) / 4 = 4/4 = 1
x₂ = (-3 – 7) / 4 = -10/4 = -2.5

So, in this case, the quadratic equation has two distinct real solutions: x = 1 and x = -2.5.

Therefore, if b²-4ac > 0, it indicates that the quadratic equation will have two distinct real solutions.

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