Complete the following activity to solve the quadratic equation by factorisation method

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Complete the following activity to solve the given quadratic equation by factorization method.

Activity: x2 + 8x – 20 = 0

x2 + ( __ ) – 2x – 20 = 0

x (x + 10) – ( __ ) (x + 10) = 0

(x + 10) ( ____ ) = 0

x = ___ or x = 2

x2 + 8x – 20 = 0

x2 + 10x – 2x – 20 = 0

∴ x (x + 10) – 2 (x + 10) = 0

∴ x (x + 10) – (x – 2) = 0

∴ x + 10 = 0 or x – 2 = 0

x = – 10 or x = 2

Concept: Solutions of Quadratic Equations by Factorization

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Solve the following quadratic equation by factorisation.

\[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\]  to solve this quadratic equation by factorisation, complete the following activity.

√2 x2 + 7 x + 5 √2 = 0
√2 x2 +

(. . . . .)(x + 2 ) = 0(. . . . .) = 0 or (x + 2 ) = 0

∴ x =

\[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\]  

\[\sqrt{2} x^2 + 5x + 2x + 5\sqrt{2} = 0\]\[x\left( \sqrt{2}x + 5 \right) + \sqrt{2}\left( \sqrt{2}x + 5 \right) = 0\]\[\left( \sqrt{2}x + 5 \right)\left( x + \sqrt{2} \right) = 0\]\[\left( \sqrt{2}x + 5 \right) = 0 \text{ or } \left( x + \sqrt{2} \right) = 0\]\[ \therefore x = \frac{- 5}{\sqrt{2}} \text{ or } x = - \sqrt{2}\]

\[ \therefore \frac{- 5}{\sqrt{2}} \text{ and } - \sqrt{2} \text{ are the roots of the equation } .\]

Concept: Solutions of Quadratic Equations by Factorization

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