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 + sqrt2) = 0`

`("______") = 0 or (x + sqrt2) = 0`

∴ x = `square or x = -sqrt2`

∴ `square` and `-sqrt(2)` are roots of the equation.

Answer 1

`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 + sqrt2) = 0`

`bb((sqrt2x+5)) = 0 or (x + sqrt2) = 0`

∴ x = `bb((-5)/sqrt2) or x = -sqrt2`

∴ `bb((-5)/sqrt2)` and `-sqrt(2)` are roots of the equation.