Answer:In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others.
Given a general quadratic equation of the form
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{\displaystyle ax^{2}+bx+c=0}
whose discriminant
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b^2 - 4ac is positive, with x representing an unknown, with a, b and c representing constants, and with a ≠ 0, the quadratic formula is:
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{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}
where the plus–minus symbol "±" indicates that the quadratic equation has two solutions.[1] Written separately, they become:
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{\displaystyle {\begin{aligned}x_{1}&={\frac {-b+{\sqrt {b^{2}-4ac}}}{2a}}\quad {\text{and}}\\x_{2}&={\frac {-b-{\sqrt {b^{2}-4ac}}}{2a}}\end{aligned}}}
Each of these two solutions is also called a root (or zero) of the quadratic equation. Geometrically, these roots represent the x-values at which any parabola, explicitly given as y = ax2 + bx + c, crosses the x-axis.[2]
As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola,[3] and the number of real zeros the quadratic equation contains.[4]
The expression b2 − 4ac is known as the discriminant. If a, b, and c are real numbers and a ≠ 0 then
If b2 − 4ac > 0 then there are two distinct real roots or solutions to the equation ax2 + bx + c = 0.
If b2 − 4ac = 0 then there is one repeated real solution.
If b2 − 4ac < 0 then there are two distinct complex solutions, which are complex conjugates of each other.
Step-by-step explanation: remeber to give 5 stars