Question

what are the roots of the function f(x)=x² + 2x - 1? x=-1±√2 x=1±2√2 x=1±√2 x=-1±2√2

Explanation:

Step1: Recall quadratic - formula

For a quadratic function $f(x)=ax^{2}+bx + c$, the roots are given by $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step2: Identify coefficients

In $f(x)=x^{2}+2x - 1$, $a = 1$, $b = 2$, and $c=-1$.

Step3: Substitute into formula

$x=\frac{-2\pm\sqrt{2^{2}-4\times1\times(-1)}}{2\times1}=\frac{-2\pm\sqrt{4 + 4}}{2}=\frac{-2\pm\sqrt{8}}{2}=\frac{-2\pm2\sqrt{2}}{2}=-1\pm\sqrt{2}$.

Answer:

$x=-1\pm\sqrt{2}$