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question 7
select all x - coordinates of x - intercepts of the graph of the function f(x)=x² + 4x + 1.
□ - 3+√2
□ - 3 - √2
□ nothing in this list is correct.
□ 3 - √2
□ 3+√2

Explanation:

Step1: Set function to zero

Set $f(x)=0$, so $x^{2}+4x + 1=0$.

Step2: Apply quadratic formula

The quadratic formula for $ax^{2}+bx + c = 0$ is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a = 1$, $b = 4$, $c = 1$. Then $x=\frac{-4\pm\sqrt{4^{2}-4\times1\times1}}{2\times1}=\frac{-4\pm\sqrt{16 - 4}}{2}=\frac{-4\pm\sqrt{12}}{2}=\frac{-4\pm2\sqrt{3}}{2}=-2\pm\sqrt{3}$. Since none of the given options match $-2\pm\sqrt{3}$.

Answer:

Nothing in this list is correct.