Question

please give me the answer ​

Answer 1

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☆ ANSWER:-

▪︎ Given quadratic equation:-

$\tt\leadsto9 {x}^{2} - 3x - 2 = 0$

▪︎ To Find:-

• The zeroes of given quadratic equation.

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▪︎ So,

• We will find out the roots by factorization and middle term splitting method.

So Here,

$\sf\mapsto Coefficient of x^2\times Constant term \\ \\ \sf = 9×2 = 18. \\ \\ \tt Also, \\ \\ \sf\mapsto 18 = 2\times 3\times 3. \\ \\ \tt And, \\ \\ \sf\mapsto (3\times 2)-3 = 6-3 \\ \\ \sf= 3 = Middle\:Term.$

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▪︎ Now, lets find out the zeroes:-

$\tt\mapsto9x {}^{2} - 3x - 2 = 0 \\ \\ \tt\mapsto9 {x}^{2} - (6 - 3)x - 2 = 0 \\ \\ \tt\leadsto 9{x}^{2} - 6x + 3x - 2 = 0 \\ \\ \tt\leadsto3x(3x - 2) + 1(3x - 2) = 0\\ \\ \tt\leadsto(3x + 1)(3x - 2) = 0 \\ \\ \tt\mapsto either \: 3x + 1 = 0 \: \: or \: \: 3x - 2 = 0 \\ \\ \tt\small\red{\fbox{\mapsto either \: x = - \frac{1}{2} \: \: or \: \: x = \frac{2}{3}}}$

▪︎ So the roots are (2/3) and (-1/3)

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$\therefore$ The Final Answer Is Option 2.

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