Answer:
-3 is the other solution.
Step-by-step explanation:
As, [tex]\frac{-4}{5}[/tex] is One of the solutions of the equations , So, it should satisfy the equation.
Putting [tex]\frac{-4}{5}[/tex] in equation 5[tex]x^{2}[/tex] + bx + 12 = 0 ,
We get,
5×[tex]\frac{-4}{5}[/tex]×[tex]\frac{-4}{5}[/tex] + b×[tex]\frac{-4}{5}[/tex] + 12 = 0.
5×[tex]\frac{16}{25}[/tex] + [tex]\frac{-4b}{5}[/tex] + 12 = 0.
After solving , 16 - 4b + 60 = 0.
4b = 76
b = 19.
So, the equation is 5[tex]x^{2}[/tex] + 19x + 12 = 0.
After factorizing , 5[tex]x^{2}[/tex] + 15x + 4x + 12 = 0.
5x(x+3) + 4(x+3) = 0
(5x+4)(x+3) = 0
Clearly the roots of the equation are -3 and [tex]\frac{-4}{5}[/tex] .
So, the other solution is -3.
