How do you factor the expression #-4 x^2-9 x -10#?

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Answer 1 · 2018-07-25T18:05:48

#-4(x+\frac{9-i\sqrt79}{8})(x+\frac{9+i\sqrt79}{8})#

#-4x^2-9x-10#

#=-(4x^2+9x+10)#

In above quadratic polynomial

#B^2-4AC=(9)^2-4(4)(10)=-79<0#

The given polynomial has no real roots hence no real factors

Now, the complex roots of #4x^2+9x+10=0# are given by quadratic formula as follow

#x=\frac{-9\pm\sqrt{9^2-4(4)(10)}}{2(4)}#

#=\frac{-9\pmi\sqrt{79}}{8}#

hence, the complex factors are given as

#-4x^2-9x-10#

#=-4(x-\frac{-9+i\sqrt79}{8})(x-\frac{-9-i\sqrt79}{8})#

#=-4(x+\frac{9-i\sqrt79}{8})(x+\frac{9+i\sqrt79}{8})#