Question

factorization method​

Answer 1

Question :-

Factories it

$\implies \sf{ {x}^{2} - 3 \sqrt{3} x + 6 = 0}$

Answer :-

→ √3 and 2√3 are factors of it .

Explanation :-

Given equation is ↓

$\rightarrow \: \sf{ {x}^{2} - 3 \sqrt{3} x + 6 = 0} \\ \\ \rightarrow \sf{ {x}^{2} - 2\sqrt{3}x - \sqrt{3} x + 6 = 0} \\ \\ \rightarrow \sf{ x(x - 2 \sqrt{3} ) - \sqrt{3} (x - 2 \sqrt{3} ) = 0} \\ \\ \rightarrow \sf{ (x - 2 \sqrt{3} )(x - \sqrt{3} ) = 0}$

• Case 1 ,if

→ x - 2√3 = 0

→ x = 2√3

• Case 2 ,if

→ x - √3 = 0

→ x = √3

Hence √3 and 2√3 are the factors of this Quadratic .

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For verification :-

One time out x = √3 ,if we get 0 then we r right .

→(√3)² - 3√3 (√3) +6 = 0

→3 - 3×3 + 6 = 0

→ -6 +6 = 0

→ 0= 0

hence verified .

now put x = 2√3 ,

→ (2√3)² - 3√3(2√3) +6 = 0

→ 4× 3 - 6×3 + 6 = 0

→ 12 -18 +6 = 0

→ -6 + 6 = 0

→ 0 = 0

hence verified.

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