Question

1. Find the roots of the quadratic eequation 6x² - X - 2 = 0

Answer 1

$\large\underline{\sf{Solution - }}$

Given equation,

$6 {x}^{2} - x - 2 = 0$

Coefficients are,

a = 6

b = –1

c = –2

Using the quadratic formulae, we get

$x = \large \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac } }{2a}$

$\implies \: x = \frac{ - ( - 1) ± \: \sqrt{( - 1)^{2} \: - 4 \: • \: 6( - 2)} }{2 \times 6}$

Simplifying the equation, we get

$\implies \: x = \frac{1±7}{12}$

Separating the equation, we get

$\implies \: x = \frac{1 + 7}{12} \: or \: \frac{1 - 7}{12}$

Now solving the equation, we get

$\therefore \: x = \frac{2}{3} \: or \: - \frac{1}{2}$

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★Another way of solving the equation,

$6 {x}^{2} - x - 2 = 0$

Factoring by splitting the middle term method.

$\implies \: 6 {x}^{2} - 4x + 3x - 2 = 0$

$\implies2x(3x-2)+1(3x-2) = 0$

$\implies \: (3x - 2)(2x + 1) = 0$

$\therefore \: x = \frac{2}{3} \: or - \frac{1 }{2}$

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