Quadratic Equation Solution
A Quadratic Equation Solution is an equation solution for a quadratic equation.
- Example(s):
- for [math]\displaystyle{ x^2-1=0 }[/math]
Let us first plot the graph of the curve [math]\displaystyle{ y=x^2-1 }[/math], which is a parabola with vertex at [math]\displaystyle{ (0,-1) }[/math]. The parabola intersects the [math]\displaystyle{ x }[/math]-axis at two points [math]\displaystyle{ x=-1 }[/math] and [math]\displaystyle{ x=1 }[/math]. So the solutions of the quadratic equation [math]\displaystyle{ x^2-1=0 }[/math] are [math]\displaystyle{ x=-1 }[/math] and [math]\displaystyle{ x=1 }[/math].
- for [math]\displaystyle{ 4x^2-8x+3=0 }[/math]
Let us first plot the graph of the curve [math]\displaystyle{ y=4x^2-8x+3 }[/math], which is a parabola with vertex at [math]\displaystyle{ (1,-1) }[/math]. The parabola intersects the [math]\displaystyle{ x }[/math]-axis at two points [math]\displaystyle{ x=1/2 }[/math] and [math]\displaystyle{ x=3/2 }[/math]. So the solutions of the quadratic equation [math]\displaystyle{ 4x^2-8x+3=0 }[/math] are [math]\displaystyle{ x=1/2 }[/math] and [math]\displaystyle{ x=3/2 }[/math].
- for [math]\displaystyle{ x^2+1=0 }[/math]
Let us first plot the graph of the curve [math]\displaystyle{ y=x^2+1 }[/math], which is a parabola with vertex at [math]\displaystyle{ (0,1) }[/math]. The parabola intersects the [math]\displaystyle{ x }[/math]-axis at no points. So there exist no real solution for the quadratic equation [math]\displaystyle{ x^2+1=0 }[/math].
- for [math]\displaystyle{ x^2-1=0 }[/math]
- Counter-Example(s):
- See: Linear Equation Solution.