Example 5 - Find roots of 3x2 - 2 root6 x + 2 = 0 - Class 10 - Solving by Splitting the middle term - Equation given

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Example 5 Find the roots of the quadratic equation 3x2 โˆ’ 2 โˆš6 ๐‘ฅ + 2 = 0 . 3x2 โ€“ 2 โˆš6 ๐‘ฅ+2=0 We will factorize using splitting the middle term method 3x2 โ€“ โˆš6 ๐‘ฅโˆ’โˆš6 ๐‘ฅ+2=0 3x2 โ€“ โˆš(2ร—3) ๐‘ฅโˆ’โˆš(2ร—3) ๐‘ฅ+2=0 3x2 โ€“ (โˆš2)(โˆš3)๐‘ฅโˆ’(โˆš2)(โˆš3)๐‘ฅ+2=0 โˆš3 ๐‘ฅ(โˆš3 ๐‘ฅโˆ’โˆš2 )โˆ’โˆš2 (โˆš3 ๐‘ฅโˆ’โˆš2 )=0 (โˆš3 ๐‘ฅ โˆ’โˆš2) (โˆš3 ๐‘ฅโˆ’โˆš2)=0 Hence x =โˆš(2/3) & x =โˆš(2/3) are roots of the equation

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