4X²-5X-12=0? - News

4x²-5x-12=0?

To solve the quadratic equation 4x^2 - 5x - 12 = 0, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 4, b = -5, and c = -12.

Substituting these values into the quadratic formula, we get:

x = (5 ± √(25 + 192)) / 8

x = (5 ± √217) / 8

So the solutions to the equation 4x^2 - 5x - 12 = 0 are:

x = (5 + √217) / 8 or x = (5 - √217) / 8

Quadratic Equations in Algebra

Quadratic equations are a fundamental topic in algebra. They are equations of the form:

ax^2 + bx + c = 0

where 'a', 'b', and 'c' are constants, and 'x' is the variable. The highest power of the variable (x^2 in this case) is 2, hence the term "quadratic."

Quadratic equations can have one of three general forms:

1. Standard Form: ax^2 + bx + c = 0
2. Vertex Form: a(x - h)^2 + k = 0
3. Factored Form: a(x - r1)(x - r2) = 0

The solutions to a quadratic equation, also known as its roots, can be found using various methods such as factoring, completing the square, or using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where ± indicates that there are generally two solutions.

Quadratic equations are incredibly important and have many applications across mathematics, physics, engineering, economics, and various other fields. They often arise in problems involving motion, optimization, and geometry, among others.