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Mathematics · Quadratic Equations · NCERT Examples

Example 5

A complete, independently verified solution for NCERT Example 5.

Mathematics · Chapter 4 · NCERT Examples

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NCERT Example

Example 5

factorisation · equal roots · radicals

Find the roots of 3x2−26x+2=0.\text{Find the roots of }3x^2-2\sqrt6x+2=0.

Solution

3x2−26x+2=3x2−6x−6x+23x^2-2\sqrt6x+2=3x^2-\sqrt6x-\sqrt6x+2
=(3x−2)2=(\sqrt3x-\sqrt2)^2
3x−2=0⇒x=23\sqrt3x-\sqrt2=0\Rightarrow x=\sqrt{\frac23}

The repeated factor gives the same root twice; substitution gives 0.

Final answer

x=23,23x=\sqrt{\frac23}, \sqrt{\frac23}