Question

Please let me know if you have any questions or concerns about math ​

Answer 1

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

$\green{\tt{\therefore{Value\:of\:a=\frac{5}{3}\:and\:-1}}}$

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

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

• According to given question :

$\bold{as \: we \: know \: that} \\ \tt: \implies {3a}^{2} - 2a - 5 = 0 \\ \\ \tt: \implies {3a}^{2} + 3a - 5a - 5 = 0 \\ \\ \tt: \implies 3a(a + 1) - 5(a + 1) = 0 \\ \\ \tt: \implies (3a - 5)(a + 1) = 0 \\ \\ \green{\tt: \implies a = \frac{5}{3} \: and \: - 1}$

$\bold{Alternate \: method} \\ \tt: \implies {3a}^{2} - 2a - 5 = 0 \\ \\ \tt \circ \: a = 3 \\ \\ \tt \circ \: b = - 2 \\ \\ \tt \circ \: c = - 5 \\ \\ \tt: \implies a = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \tt: \implies a= \frac{ - ( - 2) \pm \sqrt{( - 2)^{2} - 4 \times 3 \times ( - 5) } }{2 \times 3} \\ \\ \tt: \implies a= \frac{2 \pm \sqrt{4+ 60} }{6} \\ \\ {\tt: \implies a = \frac{2 \pm \sqrt{64} }{6}}$

$\tt: \implies a = \frac{2 \pm 8}{6} \\ \\ \green{\tt: \implies a = \frac{5}{3} \: and \: - 1}$

Answer 2

$</p><p>\tt{\huge{\purple{Hello!!! }}}$

$</p><p>\tt{\red{Given \: - }}$

$\tt{ \orange{f(x) = 3 {a}^{2} - 2a \: - 5 \: }}$

$\tt{ \purple{ \implies { 3 {a}^{2} - 5 a\: + 3a \: - 5 \: }}}$

$\tt{ \blue{ \implies {a( 3 a - 5 )\: + 1(3a \: - 5 \:) }}} \: \\ \\ \tt{ \red{ \implies{(3a - 5)(a + 1) }}}$

Hence :

$</p><p>\tt{\purple{a = \dfrac{5}{3} and -1 }}$