Respuesta :

Answer:

b=-19

Step-by-step explanation:

We know that one of the solutions is x=-4/5

That is a solution to x. So if we plug in (-4/5) into the x in the equation, then it should equal 0.

5(-4/5)^2+b(4/5)+12=0

Now, just solve for b.

5(16/25)+b(4/5)+12=0

(16/5)+(4/5)b+12=0

(76/5)+(4/5)b=0

(4/5)b=-(76/5)

b=-19
The other solution is -3

For ax^2+bx+c=0, the multiplication of the two solutions equals c/a.

Because
ax^2+bx+c=0
X^2+(b/a)x+c/a=(x-x1)(x-x2)=0 if x1 and x2 are the two solutions (roots).
(x-x1)(x-x2)=x^2-(x1+x2)x+x1*x2
The last term x1*x2 equals the last term in X^2+(b/a)x+c/a, so
X1*x2=c/a
(-4/5)*x2=12/5
x2=-3