Question

One of the solutions to the equation 5x^2+bx+12=0 is − 4/5 . Find the other solution.

Answer 1

-3 is the other solution.

Explanation:

As,
`(-4)/(5)` is One of the solutions of the equations , So, it should satisfy the equation.

Putting
`(-4)/(5)` in equation 5
`x^(2)` + bx + 12 = 0 ,

We get,

5×
`(-4)/(5)`×
`(-4)/(5)` + b×
`(-4)/(5)` + 12 = 0.

5×
`(16)/(25)` +
`(-4b)/(5)` + 12 = 0.

After solving , 16 - 4b + 60 = 0.

4b = 76

b = 19.

So, the equation is 5
`x^(2)` + 19x + 12 = 0.

After factorizing , 5
`x^(2)` + 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
`(-4)/(5)` .

So, the other solution is -3.