Question

X square + 2 root 3 x minus 24

Answer 1

Answer: -4 root 3 , 2 root 3

Step-by-step explanation:

Answer 2

$\huge\bold{Question}$


${x}^{2} + 2 \sqrt{3} x - 24$

$\huge\bold{Solution}$

Prime factorization of 24 = 2 × 2 × 2 × 3

24 can also be written as 4√2 × 2√3

Now,

${x}^{2} + 4 \sqrt{3} x - 2 \sqrt{3}x - 24 = 0 \\ \\ = > x(x + 4 \sqrt{3}) - 2 \sqrt{3} (x + 4 \sqrt{3} ) = 0 \\ \\ = > (x + 4 \sqrt{3} )(x - 2 \sqrt{3} ) = 0 \\ \\ \\ \\ x + 4 \sqrt{3} = 0 \: \: \: \: \\ \\ = > x = - 4 \sqrt{3} \\ \\ \\ x - 2 \sqrt{3} = 0 \\ \\ = > x = 2 \sqrt{3}$

$\huge \bold {answer}$

$\huge \boxed{2 \sqrt{3} \: and \: - 4 \sqrt{3} }$