Question

State whether the following quadratic equation have too distinct equal roots:
a) $(x-\sqrt{2}{)}^2-2(x+1)=0b)\sqrt{2}{x}^2-\frac{3}{\sqrt{2}}x+\frac{1}{\sqrt{2}}=0$

Answer 1

(a)$(x-\sqrt{2}{)}^2-2(x+1)=0.$

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

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

$x(x-2(\sqrt{2+1}\left)\right)=0$

it has two real and distinct roots.

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

$x^2-\frac{3}{2}x+\frac{1}{2}=0$

$\Rightarrow 2x^2-3x+1=0$

$2x^2-2x-x+1=0$

$2x(n-1)-1(n-1)=0$

$x=\frac{1}{2},1$

it has two real and distinct real roots.