Question

3x^2+kx=-3 What is the value of K will result in exactly one solution to the equation?

Answer 1

For k = 6 or k = -6, the equation will have exactly one solution.

Explanation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = (x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\bigtriangleup))/(2*a)`

`\bigtriangleup = b^(2) - 4ac`

If
`\bigtriangleup = 0`, the equation has only one solution.

In this problem, we have that:

`3x^(2) + kx + 3 = 0`

So

`a = 3, b = k, c = 3`

`\bigtriangleup = b^(2) - 4ac`

`\bigtriangleup = k^(2) - 4*3*3`

`\bigtriangleup = k^(2) - 36`

We will only have one solution if
`\bigtriangleup = 0`. So

`\bigtriangleup = 0`

`k^(2) - 36 = 0`

`k^(2) = 36`

`k = \pm √(36)`

`k = \pm 6`

For k = 6 or k = -6, the equation will have exactly one solution.