Respuesta :
The positive solution of the quadratic equation [tex]\rm 0=-x^2+2x+1[/tex] is x=2.41
It is given that the quadratic equation:
[tex]\rm 0=-x^2+2x+1[/tex]
It is required to find the solution to the above quadratic equation.
What is a quadratic equation?
A quadratic equation is a second-degree algebraic equation represented by the:
[tex]\rm ax^2+bx+c=0[/tex]........(1)
Where a, b, and c are the constants and [tex]\rm a\neq 0[/tex]
We know that:
[tex]\rm x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have:
[tex]\rm 0=-x^2+2x+1\\\rm or \\\rm -x^2+2x+1=0[/tex] ..........(2)
After comparing (1) and (2) we get:
[tex]\rm a=-1, b=2, and \ c=1[/tex]
Put these values in the above formula we get:
[tex]\rm x=\frac{-2\pm \sqrt{2^2-(4)(-1)(1)}}{(2)(-1)}\\\rm x=\frac{-2\pm \sqrt{8}}{-2}\\\rm x=\frac{-2\pm 2\sqrt{2 }}{-2}\\\rm x={1\pm \sqrt{2}}[/tex]
[tex]\rm x=1+\sqrt{2} \ or \ x=1-\sqrt{2} \\\\\sqrt{2} = 1.41\\\rm so \ x= 1+1.41 \ or \ x= 1-1.41\\\rm x=2.41 or \ x=-0.41[/tex]
Thus, the positive solution of the quadratic equation is x=2.41
Learn more about quadratic equations here:
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