Question

solve the given quadratic equation by factorization method
4√3x^2+5x-2√3=0​

Answer 1

Answer:       x = (√3/4) or, (-2/√3)

Step-by-step explanation:

    4√3 x² + 5x - 2√3  = 0

or, 4√3 x² + (8-3) x - 2√3 = 0                        as (4√3×2√3) = 24 = 8×3

or, 4√3 x² + 8x - 3x -2√3   = 0

or, 4x(√3x+2) - √3(√3x+2) = 0

or,       (4x-√3) (√3x+2)       =  0

∴ (4x- √3) = 0               ;     (√3x+2) = 0

or,    4x      = √3              or, √3x      = (-2)

or,      x      = (√3/4)         or,    x        = (-2/√3)

Answer 2

Answer:

$4 \sqrt{3} {x}^{2} + 5x - 2 \sqrt{3} = 0 \\ \\ 4 \sqrt{3} {x}^{2} + 8x - 3x - 2 \sqrt{3} = 0 \\ \\ (4 \sqrt{ 3} {x}^{2} + 8x) - (3x + 2 \sqrt{3} ) = 0 \\ \\ 4x( \sqrt{3} x + 2) - \sqrt{3} ( \sqrt{3}x + 2) = 0 \\ \\ (4x - \sqrt{3} )( \sqrt{3} x + 2) = 0 \\ \\ 4x - \sqrt{3} = 0 \: or \: \sqrt{3} x + 2 = 0 \\ \\ 4x = \sqrt{3} \: or \: \sqrt{3} x = - 2 \\ \\ x = \frac{ \sqrt{3} }{4} \: or \:x = \frac{ - 2}{ \sqrt{3} }$