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# Algebra

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What is the length of the segment of the number line whose endpoints satisfy x^2 - 16x + 3 = 0?

Dec 25, 2021

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Hello Guest!

$$x^2 - 16x + 3 = 0\\ \color{blue} x\in \{0,16\}$$

The length of the section on the x-axis is 16.

$$f(x)=x^2 - 16x + 3 \\ f'(x)=2x-16=0\\ \color{blue} x=8\\ 8^2 - 16\cdot 8 + 3 =\color{blue} -61$$

The length of the section on the axis of symmetry is 61.

!

Dec 25, 2021
edited by asinus  Dec 25, 2021