A quadratic equation, typically in the form ( ax^2 + bx + c = 0 ), is a polynomial of degree two, which means its graph is a parabola. According to the Fundamental Theorem of Algebra, a polynomial of degree ( n ) has exactly ( n ) roots (solutions) in the complex number system. Therefore, a quadratic equation has two solutions, which can be real or complex, depending on the discriminant (( b^2 - 4ac )). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution (a double root); and if it is negative, there are two complex solutions.
A quadratic equation can have either two real solutions or no real solutions.
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
To find the roots (solutions) of a quadratic equation.
Not necessarily. Formula gives two values but they can be identical.
I suggest you use the quadratic formula.
The two solutions are coincident.
A quadratic equation can have either two real solutions or no real solutions.
This formula is called the quadratic formula.
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
To find the roots (solutions) of a quadratic equation.
Not necessarily. Formula gives two values but they can be identical.
I suggest you use the quadratic formula.
The quadratic formula is x=-b (+or-) square root of b2-4ac all over 2a
Quadratic curves only have two solutions when the discrimant is greater than or equal to zero.
wew
Plug 'a', 'b', and 'c' from the equation into the formula. When you do that, the formula becomes a pair of numbers ... one number when you pick the 'plus' sign, and another number when you pick the 'minus' sign. Those two numbers are the 'solutions' to the quadratic equation you started with.
The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.