Question

Determine nature of roots of the quadratic equations.
√3 x² + 2√3 x + √3 = 0 ​

Answer 1

$\huge\underline\frak{\fbox{AnSwEr :-}}$

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Compare √3 x² + 2 √3 x + √3 = 0 with ax²+ bx + c = 0

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We get a = √3 , b = 2 √3 , c = √3 ,

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$\implies$ b² - 4 ac = (2 √3 )² - 4 x √3 x √3

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$\implies$ 4 x 3 - 4 x 3

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$\implies$ 12 - 12

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$\implies$ 0

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$\implies$ b² - 4 ac = 0

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$\therefore$ Root of the equation are real and equal.

Answer 2

$\rule{200}3$

$\huge\tt{GIVEN:}$

• a quadratic equation √3 x² + 2√3 x + √3 = 0

$\rule{200}1$

$\huge\tt{TO~FIND:}$

• The natural roots of the equation

$\rule{200}1$

$\huge\tt{SOLUTION:}$

By Comparing √3 x² + 2 √3 x + √3 = 0 with ax²+ bx + c = 0

⠀⠀⠀⠀⠀⠀⠀⠀⠀ a = √3 , b = 2 √3 , c = √3

⠀⠀⠀⠀⠀&

⠀⠀⠀⠀⠀⠀↪b² - 4ac = (2√3)² - 4 × √3 ×√3

⠀⠀⠀⠀⠀⠀↪b² - 4ac =4 × 3 - 4 × 3

⠀⠀⠀⠀⠀⠀ ↪b² - 4ac =12 - 12

⠀⠀⠀⠀⠀ ↪b² - 4ac =0

$\rule{200}3$

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