Question

3x^2-5x+2=0 by completing the square

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\alpha=\frac{2}{3}}}}$

$\green{\tt{\therefore{\beta=1}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies 3 {x}^{2} - 5x + 2 = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Value \: of \: \alpha \: and \: \beta = ?$

• According to given question :

$\tt \circ \: Let \: zeroes \: be \: \alpha \: and \: \beta \\ \\ \tt \circ \: a = 3 \\ \\ \tt \circ \: b = - 5 \\ \\ \tt \circ \: c = 2 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies 3 {x}^{2} - 5x + 2 = 0 \\ \\ \text{Both \: side \: dividing \: by \: coefficient \: of \: x}^{2} \\ \tt: \implies {x}^{2} - \frac{5}{3}x + \frac{2}{3} = 0 \\ \\ \text{Both \: side \: adding} \: (\frac{b}{2a})^{2} \\ \\ \tt\circ \: ( \frac{b}{2a}) = (\frac{ \frac{ - 5}{3} }{2 \times 1} )^{2} = \frac{25}{36} \\ \\ \tt: \implies {x}^{2} - \frac{5}{3}x + \frac{25}{36} + \frac{2}{3} = \frac{25}{36} \\ \\ \tt: \implies (x - \frac{5}{6} )^{2} = \frac{25}{36} - \frac{2}{3} \\ \\ \tt: \implies (x - \frac{5}{6} )^{2} = \frac{25 - 24}{36} \\ \\ \tt: \implies (x - \frac{5}{6} )^{2} = \frac{1}{36} \\ \\ \tt: \implies (x - \frac{5}{6} ) = \sqrt{ \frac{1}{36} } \\ \\ \tt: \implies (x - \frac{5}{6} ) = \pm\frac{1}{6} \\ \\ \tt: \implies x = \pm \frac{1}{6} + \frac{5}{6} \\ \\ \tt: \implies x = \frac{5}{6} \pm \frac{1}{6} \\ \\ \green{\tt: \implies x = \frac{5 \pm1 }{6}} \\ \\ \tt: \implies \alpha = \frac{5 - 1}{6} \\ \\ \green{\tt: \implies \alpha = \frac{2}{3} } \\ \\ \tt: \implies \beta = \frac{5 + 1}{6} \\ \\ \green{\tt: \implies \beta =1}$