Find the zeroes of the quadratic polynomial 3x2-8x+43 .

Given polynomial is

\sqrt{3} x^{2} - 8 x + 4 \sqrt{3}

.
For a polynomial

f (x

a

is said to be a root of

f

, if

f (a) = 0

.
So,

\sqrt{3} x^{2} - 8 x + 4 \sqrt{3} = 0

\Rightarrow \sqrt{3} x^{2} - 2 x - 6 x + 4 \sqrt{3}

\Rightarrow x (\sqrt{3} x - 2) - 2 \sqrt{3}

(

\sqrt{3} x - 2)

= 0

\Rightarrow (x - 2 \sqrt{3}

)(

\sqrt{3}

x-2)=0

\Rightarrow x - 2 \sqrt{3} = 0

\Rightarrow x = 2 \sqrt{3}

Or,

\Rightarrow \sqrt{3} x - 2 = 0

\Rightarrow x = \frac{2}{\sqrt{3}}

This gives,

x = 2 \sqrt{3}

x = \frac{2}{\sqrt{3}}

.
Thus, the zeroes of

\sqrt{3} x^{2} - 8 x + 4 \sqrt{3}

are

2 \sqrt{3}

and

\frac{2}{\sqrt{3}}

.
Hence, option 1 is correct.

Find the zeroes of the quadratic polynomial $\sqrt{3} x^{2} - 8 x + 4 \sqrt{3}$ .