Question

If alpha and beta are the roots of a quadratic polynomial 3x^2-6x-1 find the values of (Alpha-beta)

Answer 1

Either
`-4√(6)` or
`4√(6)`, depending on whether
`\alpha` is larger than
`\beta`.

Explanation:

The two roots (might necessarily be distinct or real) of the quadratic equation

`ax^(2) + bx + c = 0`, where
`a`,
`b`, and
`c` are constants and
`a\\e 0` are

• 
  `\displaystyle x_1 = \frac{-b+\sqrt{\text{b^(2) - 4ac}}}{2a}`, and
• 
  `\displaystyle x_2 = \frac{-b-\sqrt{\text{b^(2) - 4ac}}}{2a}`.

The difference between the two will be either:

`x_1 - x_2 = 2\sqrt{b^(2) - 4ac}` or

`x_2 - x_1 = -2\sqrt{b^(2) - 4ac}`.

For this question,

• 
  `a = 3`,
• 
  `b = -6`, and
• 
  `c = -1`.

`x_1 - x_2 = 2\sqrt{(-6)^(2) - 4* 3* (-1)} = 4√(6)`, or

`x_1 - x_2 = -2\sqrt{(-6)^(2) - 4* 3* (-1)} = -4√(6)`.