Question

The roots of quadratic equation 6 x square minus x minus 2 equal to zero Hour

Answer 1

Given:

$\sf \to 6 {x}^{2} - x - 2 = 0$

Find:

$\sf \to find \: roots \: of \: eq. \: 6 {x}^{2} - x - 2 = 0$

Solution:

we, have

$\sf \longrightarrow 6 {x}^{2} - x - 2 = 0$

Solve, by middle-split term

$\sf \longrightarrow 6 {x}^{2} - x - 2 = 0$

$\sf \longrightarrow 6 {x}^{2} - 4x + 3x- 2 = 0$

$\sf \longrightarrow 2x(3x - 2) + 1(3x- 2) = 0$

$\sf \longrightarrow (2x + 1)(3x- 2) = 0$

$\sf \begin{gathered} \sf 2x + 1 = 0 \\ \sf 2x = - 1 \\ \sf x = \dfrac{ - 1}{2} \end{gathered} \qquad\begin{gathered} \sf 3x- 2 = 0 \\ \sf 3x = 2 \\ \sf x = \dfrac{ 2}{3} \end{gathered}$

Therefore, roots of quadratic eq. 6x² - x - 2 = 0 are -1/2 and 2/3