Question

Solve the following equation by the method of completing the square: 4√3x^2 + 5x - 2√3 = 0

Answer 1

4√3x^2+8x-3x-2√3
4x(√3x+2)-√3(√3x+2)
(4x-√3) (√3x+2)

x=√3/4
and x=-2/√3

Answer 2

hi mate,

=4√3x²+5x-2√3

=4√3x² + 8x - 3x - 2√3

=4x(√3x +2) - √3(√3x + 2)

=(4x - √3) ( √3x + 2)

⇒4x - √3 =0 or ⇒√3x

+2=0

⇒ x = √3/4 or ⇒ x= -2√3

4.4

p(x) = 4√3x² + 5x - 2√3

p(x) = 4√3x² + 8x - 3x - 2√3 ( SPLITTING THE MIDDLE TERM)

p(x) = 4x(√3x + 2 ) - √3 ( √3x + 2)

p(x) = ( √3x+2 ) ( 4x-√3 )

p(x) = 0

( √3x+2 ) ( 4x-√3 ) = 0

√3x+2 = 0 or 4x-√3 = 0

x = -2/√3 or, x = √3/4

VERIFICATION :-

Hence, the zeroes of p(x) are :

∝ = -2/√3 and β = √3/4

Now, ∝ + β = -2/√3 + √3/4

-8+3/4√3

-5/4√3

And

∝β = -2/√3 × √3/4

= -1`/2

Now, from equation :- ( 4√3x² + 5x - 2√3.)

a = 4√3

b = 5

c = -2√3

∝ + β = -b/a

⇒ -5/4√3

And

∝β = c/a

-2√3/4√3

⇒ -1/2