Solve the following quadratic equations by factorization: √3x^2 - 2√2x - 2√3 = 0

Question

Solve the following quadratic equations by factorization:

\(\sqrt{3}x^{2}-2\sqrt{2}x-2\sqrt{3}=0\)

Answer 1

In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

\(\sqrt{3}x^{2}-2\sqrt{2}x-2\sqrt{3}=0\)

⇒ √3x² – 3√2x + √2x – 2√3 = 0 

⇒ √3x² – √3×√3×√2x + √2x – 2×√3×√3 = 0

⇒ √3x² – √3×√6x + √2x – √6×√3 = 0 

⇒ √3x(x - √6) + √2(x - √6) = 0 

⇒ (√3x + √2)(x - √6) = 0 

⇒ x = √6, -√(2/3)