Question

complete the square :
4x*2 + 4 root 3x + 3 = 0
Pls answer me fast pls pls take the photo of the solution ​

Answer 1

Given :

• 4x² + 4√3x + 3 = 0

Solution :

• Method ➊
• Solve this question by quadratic formula

According to quadratic formula

→ D = b² - 4ac

• a = 4
• b = 4√3
• c = 3

→ D = (4√3)² - 4 × 4 × 3

→ D = 16 × 3 - 48

→ D = 48 - 48

→ D = 0

Now,

→ x = - b ± √D/2a

Either

→ x = - 4√3 + 0/2 × 4

→ x = - 4√3/2 × 4

→ x = - √3/2

Or

→ x = - 4√3 - 0/2 × 4

→ x = -4√3/2 × 4

→ x = - √3/2

Focus Zone : Discriminant (D) is zero. It shows that the solutions of given equation are equal.

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• Method ➋

Splitting middle term

→ 4x² + 4√3x + 3 = 0

→ 4x² + 2√3x + 2√3x + 3 = 0

→ 2x(2x + √3) + √3(2x + √3) = 0

→ (2x + √3)(2x + √3) = 0

•°• x = -√3/2 and - √3/2

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Answer 2

Required Answer:-

$\\ \hookrightarrow \tt \: {4x}^{2} + \sqrt[4]{3x} + 3 = 0$

$\bigstar$By splitting the middle term,

$\\ \hookrightarrow \tt \: {4x}^{2} + \sqrt[2]{3x} + \sqrt[2]{3x} + 3 = 0$

$\\ \hookrightarrow \tt \:2x \times \left(2x + \sqrt{3} \right) + \sqrt{3} \times \left(2x + \sqrt{3} \right) = 0$

$\\ \hookrightarrow \tt\left(2x + \sqrt{3} \right) + \left(2x + \sqrt{3} \right) = 0$

$\\ \hookrightarrow \tt \: \left(2x + \sqrt{3} \right) = 0$

$\\ \hookrightarrow \tt \: 2x = \sqrt{ - 3}$

$\\ \hookrightarrow \tt \: x = \frac{ \sqrt{ - 3} }{2}$