Question

Factor the expression -35x^2-41x-12

Answer 1

`ax^2+bx+c\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ ax^2+bx+c=a(x-x_1)(x-x_2)\ where\ x_(1;2)=(-b\pm\sqrt\Delta)/(2a)\\\========================================`


`-35x^2-41x-12\\\\a=-35;\ b=-41;\ c=-12\\\\\Delta=(-41)^2-4\cdot(-35)\cdot(-12)=1681-1680=1 > 0\\\\\sqrt\Delta=\sqrt1=1\\\\x_1=(-(-41)-1)/(2\cdot(-35))=(41-1)/(-70)=(40)/(-70)=-(4)/(7)\\\\x_2=(-(-41)+1)/(2\cdot(-35))=(41+1)/(-70)=(42)/(-70)=-(21)/(35)=-(3)/(5)\\\\therefore:\\\\\boxed{-35x^2-41-12=-35\left(x+(4)/(7)\right)\left(x+(3)/(5)\right)}`