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Question
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
(______) (x + 2) = 0
(______) = 0 or (x + 2) = 0
∴ x = `square` or x = - 2
∴ `square` and `sqrt(-2)` are roots of the equation.
Solution
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+bb(5x)+bb(2x)+5sqrt2=0`
`xbb((sqrt2x+5)) + sqrt2 bb((sqrt2x+5)) = 0`
`bb((sqrt2x+5)) (x + 2) = 0`
`bb((sqrt2x+5)) = 0 or (x + 2) = 0`
∴ x = `bb(-5/sqrt2)` or x = -2
∴ `bb(-5/sqrt2)` and `sqrt(-2)` are roots of the equation.
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