[latex]ax^2+bx+c=a(x-x_1)(x-x_2)[/latex][latex]D=b^2-4ac[/latex][latex]x_1=frac{-b-sqrt{D}}{2a}[/latex][latex]x_2=frac{-b+sqrt{D}}{2a}[/latex]---[latex]4c^2+7c-2=0[/latex][latex]D=7^2-4*4*(-2)=49+32=81=9^2[/latex][latex]c_1=frac{-7-9}{2*4}=-2[/latex][latex]c_2=frac{-7+9}{2*4}=frac{1}{4}[/latex][latex]4c^2+7c-2=4(c-(-2))(c-frac{1}{4})=(c+2)(4c-1)[/latex]----------------------------------[latex]1-16c^2=1^2-(4c)^2=(1-4c)(1+4c)=-(4c+1)(4c-1)[/latex]------------------------------[latex]frac{4c^2+7c-2}{1-16c^2}=frac{(c+2)(4c-1)}{-(4c+1)(4c-1)}=\\-frac{c+2}{4c+1}[/latex]