Question

For what values of m mx^2 + (3x-1)m + 2x +5 = 0 have equal roots but opposite sign ?

Answer 1

Use the discriminant to find out the count of the roots of following equations:

 x2–14x +33=0 D=(-14)2-4.1.33=64Two different roots in real numbers 4x2–5x+1=0 D=(-5)2-4.4.1=9Two different roots in real numbers x2–10x+25=0 D=(-10)2-4.1.25=0One (double) root in real numbers 12x2–5x-3=0 D=(-5)2-4.12.(-3)=169Two different roots in real numbers x2–4x+13=0 D=(-4)2-4.1.13=–36No solution in real numbers x2–14x+49=0 D=(-14)2–4.1.49=0One (double) root in real numbers x2–6x+25=0 D=(-6)2-4.1.25=–64No solution in real numbers

Answer 2

-(2x+5)/(x-1)(2x+1)

hope it will be right