paulmdrdo said:please help me with this
$\frac{x^2+2}{x}+\frac{8x}{x^2+2}=6$
this is where I can get to when I simplify the the equation above,
$x^4-6x^3+12x^2+12x+4=0$
paulmdrdo said:please help me with this
$\frac{x^2+2}{x}+\frac{8x}{x^2+2}=6$
this is where I can get to when I simplify the the equation above,
$x^4-6x^3+12x^2+12x+4=0$
A quadratic equation is an algebraic equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is a second degree polynomial equation and can have two possible solutions.
The most common method for solving a quadratic equation is by using the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. This formula gives the values of x that satisfy the equation. Another method is by factoring the equation into two linear factors and solving for x.
The discriminant is the part of the quadratic formula under the square root, b^2 - 4ac. It is used to determine the nature of the solutions of the equation. If the discriminant is positive, the equation has two distinct real solutions. If it is zero, the equation has one real solution. And if it is negative, the equation has two complex solutions.
Yes, quadratic equations can have non-integer solutions, also known as irrational or fractional solutions. These solutions cannot be expressed as a simple fraction or decimal and often involve the square root of a non-perfect square number.
Quadratic equations are used in various fields such as physics, engineering, and finance to model real-life situations. For example, they can be used to calculate the trajectory of a projectile, determine the optimal dimensions of a structure, or calculate the maximum profit for a business. They are also used in computer graphics to create smooth curves and surfaces.