Question

Solve the following quadratic equation by factorization, the roots are
$x^2-(\sqrt{3}+1)x+\sqrt{3}=0$

• A. $3$, $1$
• B. $\sqrt{2}$, $1$
• C. $\sqrt{3}$, $1$
• D. $\sqrt{5}$, $1$

Answer 1

Answer: (C)

$\sqrt{3}$, $1$

consider, $x^2-(\sqrt{3}+1)x+\sqrt{3}=0$

$\Rightarrow$ $x^2-\sqrt{3}x-x+\sqrt{3}=0$

$\Rightarrow$ $x(x-\sqrt{3})-1(x-\sqrt{3})=0$

$\Rightarrow$ $(x-\sqrt{3})(x-1)=0$

$\Rightarrow$ $x-\sqrt{3}=0$ and $x-1=0$

$\Rightarrow$ $x=\sqrt{3}$ and $x=1$