Find the roots of the quadratic equation- 3 x2-2 -6 x-2-2 -6-0-

3x^2 2√(6)+2 =0 ⇒ 3x^2 √(6)x √(6)x+2 =0 ⇒√(3)x[√(3)x √(2)] √(2)[√(3)x √(2)]=0 ⇒ [√(3)x √(2)][√(3)x √(2)]=0 ⇒ [√(3)x √(2)]=0 or [√(3)x √(2)]=0 ⇒ x =√(2)/√(3) o ...

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Find the roots of the quadratic equation, $\frac{3 x^{2} - 2 \sqrt{6} x + 2}{2 \sqrt{6}} = 0$ .

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Solution

$3 x^{2} - 2 \sqrt{6} + 2 = 0 \Rightarrow 3 x^{2} - \sqrt{6} x - \sqrt{6} x + 2 = 0 \Rightarrow \sqrt{3} x [\sqrt{3} x - \sqrt{2}] - \sqrt{2} [\sqrt{3} x - \sqrt{2}] = 0 \Rightarrow [\sqrt{3} x - \sqrt{2}] [\sqrt{3} x - \sqrt{2}] = 0 \Rightarrow [\sqrt{3} x - \sqrt{2}] = 0 o r [\sqrt{3} x - \sqrt{2}] = 0 \Rightarrow x = \frac{\sqrt{2}}{\sqrt{3}} o r x = \frac{\sqrt{2}}{\sqrt{3}}$
So. $x = \frac{\sqrt{2}}{\sqrt{3}}, \frac{\sqrt{2}}{\sqrt{3}}$ is the solution.

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Find the roots of the quadratic equation, 3x2−2√6x+22√6=0.

3x2−2√6+2=0⇒3x2−√6x−√6x+2=0⇒√3x[√3x−√2]−√2[√3x−√2]=0⇒[√3x−√2][√3x−√2]=0⇒[√3x−√2]=0or[√3x−√2]=0⇒x=√2√3orx=√2√3 So. x=√2√3,√2√3 is the solution.

Find the roots of the quadratic equation, $\frac{3 x^{2} - 2 \sqrt{6} x + 2}{2 \sqrt{6}} = 0$ .