If b²-4ac > 0
There are 2 real roots
If b²-4ac > 0, the quadratic equation ax²+bx+c has two distinct real roots.
The expression b²-4ac is known as the discriminant of the quadratic equation. If the discriminant is greater than zero, it means that there are two distinct real roots of the given quadratic equation.
To understand why, we need to consider the quadratic formula, which is given by:
x = (-b ± √(b²-4ac)) / 2a
The square root of the discriminant is present within this formula. If the discriminant is greater than zero, then the square root expression will have two real values, one positive and one negative. This means that we will get two distinct solutions for x when we solve the quadratic equation.
For example, let’s say we have the quadratic equation x²-6x+5 = 0. The coefficients are a=1, b=-6, and c=5. We can calculate the discriminant as follows:
b²-4ac = (-6)² – 4(1)(5) = 36 – 20 = 16
Since the discriminant is greater than zero, we know that there will be two distinct real roots to this equation. We can use the quadratic formula to find these roots:
x = (-(-6) ± √(16)) / 2(1)
x = (6 ± 4) / 2
x = 5 or x = 1
Therefore, the roots of the equation x²-6x+5 = 0 are x=5 and x=1, both of which are real and distinct.
More Answers:
Determining The Properties And Applications Of The Exponential Function F(X) = D E^XDiscover Why B²-4Ac = 0 Results In One Real Root For Quadratic Equations
The Quadratic Equation: How A Negative Discriminant Leads To Complex Roots