Question

Factor the following trinomial. (Hint: Solve the equations first.) x²-2x-2

Answer 1

Answer:

$(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))$  

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} -2x-2=0$  

so

$a=1\\b=-2\\c=-2$

substitute in the formula

$x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}$

$x=\frac{2(+/-)\sqrt{12}} {2}$

$x=\frac{2(+/-)2\sqrt{3}} {2}$

$x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}$

$x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}$

therefore

$x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))$