Example 5 - Chapter 4 Class 10 Quadratic Equations (Important Question)

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Example 5 Find the roots of the quadratic equation 3x2 − 2 √6 𝑥 + 2 = 0 . 3x2 – 2 √6 𝑥+2=0 We will factorize using splitting the middle term method 3x2 – √𝟔 𝒙−√𝟔 𝒙+𝟐=𝟎 3x2 – √(2×3) 𝑥−√(2×3) 𝑥+2=0 3x2 – (√2)(√3)𝑥−(√2)(√3)𝑥+2=0 √3 𝑥(√3 𝑥−√2 )−√2 (√3 𝑥−√2 )=0 (√𝟑 𝒙 −√𝟐) (√𝟑 𝒙−√𝟐)=𝟎 √3 𝑥 −√2 = 0 √3 𝑥 = √2 x = √𝟐/√𝟑 = √(𝟐/𝟑) √3 𝑥 −√2 = 0 √3 𝑥 = √2 x = √𝟐/√𝟑 = √(𝟐/𝟑) Hence, x =√(𝟐/𝟑) & x =√(𝟐/𝟑) are roots of the equation