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Question

# Factorize √3 x2 + 5x + 2√3 = 0 by splitting the middle term and find the value of x.

A

x=233,x=3

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B

x=233,x=3

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C

x=233,x=3

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D

x=233,x=3

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Solution

## The correct option is A x=−2√33,x=−√3 Multiply √3 with 2√3 and we get 6 Factors of 6 are 1×6 = 6 sum 1+ 6 = 7 2×3= 6 sum 2+ 3 = 5 So our required pair of factors is 2 and 3 ⇒√3x2+5x+2√3=0 ⇒√3x2+3x+2x+2√3=0 ⇒√3x(x+√3)+2(x+√3)=0 ⇒(√3x+2)(x+√3)=0 ∴ Factors are (√3x+2),(x+√3) ⇒(√3x+2)=0 and (x+√3)=0 ⇒x=−2√3 and x=−√3 Rationalising the denominator x=−2√3 × √3√3 x=−2√33

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