Question

In the equation kx^2 + 5x = 10k, find the other root if one root is -5.

Answer 1

Subtract 10k from both sides:

`kx^2+5x-10k = 0`

Assuming
`k\\eq 0`, divide both sides by k:

`x^2+(5)/(k)x-10 = 0`

When you write a quadratic equation as
`x^2-sx+p`, you know that the two solutions follow the properties

`x_1+x_2=s,\quad x_1x_2=p`

So, in this case, we have

`x_1+x_2=-(5)/(k),\quad x_1x_2=-10`

Since we know that
`x_1=-5` we have:

`\begin{cases}-5+x_2=-(5)/(k)\\ -5x_2=-10\end{cases}`

This system has solution
`k=(5)/(3),\ x=2`

Answer 2

2

Explanation:

One root = -5

We know ,

• Product of roots = c/a
• -5 * x = -10k / k
• -5x = -10
• x = 2

Other root is 2 .