Question

x^2+3√3x+6 by mid term spilt

Answer 1

Answer

(x + √3)(x + 2√3) is the factorized form .

-√3 and -2√3 are the zeroes of the polynomial .

Step-by-step explanation:

Given ,

${x}^{2} + 3 \sqrt{3}x + 6$

Now Splitting the middle term :

${x}^{2} + \sqrt{3} x + 2 \sqrt{3}x + 6 \\ \\ = x(x + \sqrt{3} ) + 2 \sqrt{3} (x + \sqrt{3} ) \\ \\ =( x + \sqrt{3} )(x + 2 \sqrt{3} )$

Factorized

_______________________________

If we find the zeroes of the above quadratic polynomial then :

$x + \sqrt{3} = 0 \\ \implies \: x = - \sqrt{3}$

And

$x + 2 \sqrt{3} = 0 \\ \implies \: x = - 2\sqrt{3}$