Question

find the zeroes of x²+3√3x+6​

Answer 1

Answer:

Zeroes of the expression are -√3 and -2√3

Step-by-step explanation:

$x^2+3\sqrt3x+6=0\\\implies x^2+\sqrt3x+2\sqrt3x+6=0\\\implies x(x+\sqrt3)+2\sqrt3(x+\sqrt3)=0\\\implies (x+2\sqrt3)(x+\sqrt3)=0$

If

$x+2\sqrt3=0\\\implies x=-2\sqrt3$

If

$x+\sqrt3=0\\\implies x=-\sqrt3$

So,

$x=\{-\sqrt3,-2\sqrt3\}$

Hope it helps!

<3

Answer 2

Answer:

x²+3√3x+6 = (x+2√3)(x+√3)

Explanation:

Given quadratic expression:

x²+3√3x+6

Splitting the middle term, we get

=x²+2√3x+√3x+6

= x²+2√3x+√3x+2×√3×√3

= x(x+2√3)+√3(x+2√3)

= (x+2√3)(x+√3)

Therefore,

x²+3√3x+6 = (x+2√3)(x+√3)