Question

obtain the roots of the following equation using the method of completing square:
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Answer 1

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☆ ANSWER:-

▪︎ Given equation:-

$\tt\leadsto3 {y}^{2} + 7y - 20$

▪︎ To Find:-

• The roots of the equation by completing square method.

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▪︎ So,

• Firstly let us divide the whole equation by 3 to make the calculation easy:-

$\tt\leadsto \frac{3 {y}^{2} + 7y - 20 = 0 }{3} \\ \\ \tt\leadsto {y}^{2} + \frac{7y}{3} - \frac{20}{3} = 0$

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▪︎ Now,

• Lets find the roots of the equation by completing square method-:

$\sf\mapsto {y}^{2} + \frac{7y}{3} - \frac{20}{3} = 0 \\ \\ \sf \mapsto {y}^{2} + \frac{7y}{3} = \frac{20}{3} \\ \\ \sf \mapsto {(y)}^{2} + 2 \times y \times \frac{7}{6} + ( \frac{7}{6}) {}^{2} = \frac{20}{3} + (\frac{7}{6} ) {}^{2} \\ \\ \sf \mapsto(y + \frac{7}{6}) {}^{2} = \frac{20}{3} + \frac{49}{36} \\ \\ \sf \mapsto(y + \frac{7}{6} ) {}^{2} = \frac{(20 \times 12) + 49}{36} \\ \\ \tt ( taking \: lcm) \\ \\ \sf \mapsto(y + \frac{7}{6}) {}^{2} = \frac{240 + 49}{36} \\ \\ \sf \mapsto(y + \frac{7}{6} ) {}^{2} = \frac{289}{36} \\ \\ \sf \mapsto(y + \frac{7}{6} ) {}^{\cancel{2} } = \frac{ + }{} ( \frac{17}{6} ) {}^{\cancel{2} } \\ \\ \sf \mapsto \: y + \frac{7}{6} = \frac{ + }{} \: \frac{17}{6} \\ \\ \sf \mapsto \: y = \frac{ + }{} \: \frac{17}{6} - \frac{7}{6} \\ \\ \sf \mapsto \: y = \frac{ 17 - 7 }{6} \: \: or \: \: y = \frac{ - 17 - 7}{6} \\ \\ \sf \mapsto \: y = \cancel \frac{10}{6} \: \: or \: \: y = \cancel \frac{ - 24}{6} \\ \\ \sf \large\red{\fbox{\mapsto \: y = \frac{5}{3} \: \: or \: \: y = - 4}}$

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${\small{\green{\boxed{\bold{\mathcal{\therefore{The\:req.\:Roots\:are\:5/3\:And\:-4.}}}}}}}$

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