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

Answer:Either [tex]-4\sqrt{6}[/tex] or [tex]4\sqrt{6}[/tex], depending on whether [tex]\alpha[/tex] is larger than [tex]\beta[/tex].Step-by-step explanation:The two roots (might necessarily be distinct or real) of the quadratic equation[tex]ax^{2} + bx + c = 0[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are constants and [tex]a\ne 0[/tex] are[tex]\displaystyle x_1 = \frac{-b+\sqrt{\text{b^{2} - 4ac}}}{2a}[/tex], and[tex]\displaystyle x_2 = \frac{-b-\sqrt{\text{b^{2} - 4ac}}}{2a}[/tex].The difference between the two will be either:[tex]x_1 - x_2 = 2\sqrt{b^{2} - 4ac}[/tex] or[tex]x_2 - x_1 = -2\sqrt{b^{2} - 4ac}[/tex].For this question,[tex]a = 3[/tex], [tex]b = -6[/tex], and[tex]c = -1[/tex].[tex]x_1 - x_2 = 2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = 4\sqrt{6}[/tex], or[tex]x_1 - x_2 = -2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = -4\sqrt{6}[/tex].