Understanding the Discriminant: Exploring the Nature of Roots in Quadratic Equations

If b²-4ac > 0

If b²-4ac > 0, this means that the discriminant of the quadratic equation ax²+bx+c = 0 is positive

If b²-4ac > 0, this means that the discriminant of the quadratic equation ax²+bx+c = 0 is positive. The discriminant is the expression inside the square root (√) when solving for the roots of a quadratic equation using the quadratic formula.

When the discriminant is greater than 0, it indicates that the quadratic equation has two distinct real roots. The value of b²-4ac provides information about the nature of the roots of the quadratic equation.

To find the roots of a quadratic equation, we can use the quadratic formula:

x = (-b ± √(b²-4ac))/(2a)

Here, “x” represents the roots of the equation, “a,” “b,” and “c” are the coefficients of the quadratic equation.

When b²-4ac is greater than 0, the expression inside the square root (√) is positive. Therefore, we have two solutions or roots for the equation. These two roots may be rational or irrational numbers.

For example, let’s say we have the quadratic equation 2x²+3x-4 = 0. By comparing the coefficients, we have a=2, b=3, and c=-4. We can find the discriminant as follows:

b²-4ac = (3)² – 4(2)(-4)
= 9 + 32
= 41

Since the discriminant is greater than 0 (41 > 0), we know that this quadratic equation has two distinct real roots.

Finally, we can find the roots using the quadratic formula:

x = (-3 ± √41)/(2*2)

So, the roots will be:

x₁ = (-3 + √41)/4
x₂ = (-3 – √41)/4

These are the solutions to the quadratic equation when b²-4ac is greater than 0.

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