Question

Find the zeroes of the polynomial 4 root 3x2 + 5x -2 root.3.

Answer 1

=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

Answer 2

$\huge{\boxed{\mathbb{ANSWER}}}$

To Find : The zeroes of the polynomial 4√3x² + 5x - 2√3.

We are having :

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

Hence, Verified!