Question

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Answer 1

Answer: About (-2.414, 0) and (0.414, 0)

Step-by-step explanation:

       Let us graph the equation given and see what the x-intercepts are. These are points where the line intercepts the x-axis. See attached.

       This means our x-intercepts are at about (-2.414, 0) and (0.414, 0).

                        These are also equal to $-1-\sqrt{2}$ and  $-1+\sqrt{2}$

Answer 2

Answer:

$x = \bold{0.414} \textrm{ and } x= \bold{-2.414}$

Step-by-step explanation:

See attached graph for a visual

The x-intercepts of a graph are where the graph crosses the x-axis ie where the value of y = 0 The equation of the graph is y=-x^{2}-2x+1

Setting y = 0 and solving for the resultant equation will provide the x-intercepts

$0=-x^{2}-2x+1or-x^{2}-2x+1=0$

Reversing the signs gives us

$x^{2}+2x-1=0$

This is a quadratic equation of the form $ax^{2}+bx+c=0$ with a = 1, b = 2 and c=-1

For an equation of this form the roots of the equation ie the values of x which satisfy the equation are given by

$\frac{-b\pm\sqrt{{b^{2}-4ac}}}{2a}$

Substituting we get the two roots as

$x=\frac{-2\pm\sqrt{{2^{2}-4(1)(-1}}}{2}=\frac{-2\pm\sqrt{{4-(-4)}}}{2}x=\frac{-2\pm\sqrt{8}}{2}8 = 4(2)\sqrt{8}=\sqrt{4}\sqrt{2} = 2\sqrt{2}$

So the two roots are

$x=\frac{-2\pm2\sqrt{2}}{2}$

Dividing by 2 we get the two roots(x-intercepts) as

$x=-1\pm\sqrt{2}\\\\x_{1}=-1+\sqrt{2} =-1+1.414=\bold{0.414}$

$x_{2}=-1-\sqrt{2}=-1-1.414=\boldsymbol{-2.414}$