Math, asked by rewa66, 10 months ago

please solve.......

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Answered by hritikVK18

1. X =4 & - 2

2.X=2,2

3.X=9,2

Answered by abdul9838

$<b> <body bgcolor = "sky blue"> <font color = "red">$

$\small \bf{hey \: mate \: here \: is \: ur \: ans} \\ \\ \small \bf \red{ \huge \: solution} \\ \\ \small \bf \red{ {x}^{2} - 2x - 8 = 0 } \\ \\ \small \bf \red{ {x}^{2} - (4 - 2)x - 8 = 0 } \\ \\ \small \bf \red{ {x}^{2} - 4x + 2x - 8 = 0} \\ \\ \small \bf \red{x(x - 4) + 2(x - 4) = 0} \\ \\ \small \bf \red{(x + 2)(x - 4) = 0} \\ \\ \small \bf \red{x = - 2} \\ \\ \small \bf \red{and} \\ \\ \small \bf \red{x = 4} \\ \\ \small \bf \red{let \: be} \\ \\ \small \bf \red{ \alpha = - 2} \\ \\ \small \bf \red{ \beta = 4} \\ \\ \small \bf \red{ \huge \: now} \\ \\ \small \bf \red{ \underline{sum \: of \: zeros} = - \frac{b(where \: b \: cofficient \: of \: x)}{a(where \: a \: cofficient \: of \: {x}^{2}) } } \\ \\ \small \bf \red{ \alpha + \beta = - \frac{b}{a} } \\ \small \bf \red{ - 2 + 4 = - \frac{( - 2)}{1} } \\ \\ \small \bf \red{2 = 2} \\ \\ \small \bf \red{ \underline{product \: of \: zeros} = \frac{c}{a} } \\ \\ \small \bf \red{ \alpha \times \beta = \frac{c(where \: c \: constant \: term)}{a(cofficient \: of \: {x}^{2} )} } \\ \\ \small \bf \red{ - 2 \times 4 = - \frac{8}{1} } \\ \\ \small \bf \red{ - 8 = - 8} \\ \\ 2... \\ \\ \small \bf \red{4 {s}^{2} - 4s + 1 = 0} \\ \\ \small \bf \red{4 {s}^{2} - (2 + 2)s + 1 = 0} \\ \\ \small \bf \red{4 {s}^{2} - 2s - 2s + 1 = 0 } \\ \\ \small \bf \red{2s(2s - 1) - 1(2s - 1) = 0} \\ \\ \small \bf \red{(2s - 1)(2s - 1) = 0} \\ \\ \small \bf \red{s = \frac{1}{2} } \\ \\ \small \bf \red{and} \\ \\ \small \bf \red{s = \frac{1}{2} } \\ \\ \small \bf \red{let \: be \: } \\ \\ \small \bf \red{ \alpha = \frac{1}{2} } \\ \\ \small \bf \red{ \beta = \frac{1}{2} } \\ \\ \small \bf \red{ \underline{sum \: of \: zeros} = - \frac{b}{a} } \\ \\ \small \bf \red{ \alpha + \beta = - \frac{b}{a} } \\ \\ \small \bf \red{ \frac{1}{2} + \frac{1}{2} = - \frac{( - 4)}{4} } \\ \\ \small \bf \red{ \frac{2}{2} = 1 } \\ \\ \small \bf \red{1 = 1} \\ \\ \small \bf \red{ \underline{product \: of \: zeros } = \frac{c}{a} } \\ \\ \small \bf \red{ \alpha \times \beta = \frac{c}{a} } \\ \\ \small \bf \red{ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} } \\ \\ \small \bf \red{ \frac{1}{4} = \frac{1}{4} } \\ \\ 3.. \\ \\ \small \bf \red{6 {x}^{2} - 7x - 3 = 0 } \\ \\ \small \bf \red{6 {x}^{2} - (9 - 2)x - 3 = 0 } \\ \\ \small \bf \red{6 {x}^{2} - 9x + 2x - 3 = 0} \\ \\ \small \bf \red{3x(2x - 3) + 1(2x - 3) = 0} \\ \\ \bf\red{(3x + 1)(2x - 3) = 0} \\ \\ \small \bf \red{ = - \frac{1}{3} } \\ \\ \small \bf \red{x = \frac{3}{2} } \\ \\ \small \bf \red{let \: be} \\ \\ \small \bf \red{ \alpha = - \frac{1}{3} } \\ \\ \small \bf \red{ \beta = \frac{3}{2} } \\ \\ \small \bf \red{ \underline{sum \: of \: zeros} = - \frac{b}{a} } \\ \\ \small \bf \red{ \alpha + \beta = - \frac{b}{a} } \\ \\ \small \bf \red{ - \frac{1}{3} + \frac{3}{2} = - \frac{ - (7)}{6} } \\ \\ \small \bf \red{ \frac{ - 2 + 9}{6} = \frac{7}{6} } \\ \\ \small \bf \red{ \frac{7}{6} = \frac{7}{6} } \\ \\ \small \bf \red{ \underline{product \: of \: zeros} = \frac{c}{a} } \\ \\ \small \bf \red{ \alpha \times \beta = \frac{c}{a} } \\ \\ \small \bf \red{ - \frac{1}{3} \times \frac{3}{2} = - \frac{3}{6} } \\ \\ \small \bf \red{ - \frac{1}{2} = - \frac{1}{2} \: \: ans }$

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