Answer:
Given a general quadratic equation of the form
{\displaystyle ax^{2}+bx+c=0}ax^2+bx+c=0
with x representing an unknown, a, b and c representing constants with a ≠ 0, the quadratic formula is:
{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }{\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:
{\displaystyle x_{1}={\frac {-b+{\sqrt {b^{2}-4ac}}}{2a}}\quad {\text{and}}\quad x_{2}={\frac {-b-{\sqrt {b^{2}-4ac}}}{2a}}}{\displaystyle x_{1}={\frac {-b+{\sqrt {b^{2}-4ac}}}{2a}}\quad {\text{and}}\quad x_{2}={\frac {-b-{\sqrt {b^{2}-4ac}}}{2a}}}
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]
Step-by-step explanation:
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