Question

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

Answer 1

Answer:

Either $-4\sqrt{6}$ or $4\sqrt{6}$, depending on whether $\alpha$ is larger than $\beta$.

Step-by-step 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 $a\ne 0$ 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
• $c = -1$.

$x_1 - x_2 = 2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = 4\sqrt{6}$, or

$x_1 - x_2 = -2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = -4\sqrt{6}$.