In the given #160;quadratic #160;polynomial 4x^ 2 +4√( 3 ) x+3=0 ,The first term is #160; 4x^2 #160;and its coefficient is #160; 4 .The ...

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Factorisation by Common Factors

4x2+4√3x+3=0.

Question

$4 x^{2} + 4 \sqrt{3} x + 3 = 0$ .

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Solution

In the given quadratic polynomial $4 x^{2} + 4 \sqrt{3} x + 3 = 0$ ,
The first term is $4 x^{2}$ and its coefficient is $4$ .
The middle term is $4 \sqrt{3} x$ and its coefficient is $4 \sqrt{3}$ .
The last term is a constant term $3$ .

Multiply the coefficient of the first term by the constant $4 \times 3 = 12$ .

We now find the factor of $12$ whose sum equals the coefficient of the middle term, which is $4 \sqrt{3}$ and then factorize the quadratic polynomial $4 x^{2} + 4 \sqrt{3} x + 3 = 0$ as shown below:
$4 x^{2} + 4 \sqrt{3} x + 3 = 0 \Rightarrow 4 x^{2} + 2 \sqrt{3} x + 2 \sqrt{3} x + 3 = 0 \Rightarrow 2 x (2 x + \sqrt{3}) + \sqrt{3} (2 x + \sqrt{3}) = 0 \Rightarrow (2 x + \sqrt{3}) (2 x + \sqrt{3}) = 0 \Rightarrow (2 x + \sqrt{3}) = 0, (2 x + \sqrt{3}) = 0 \Rightarrow 2 x = - \sqrt{3}, 2 x = - \sqrt{3} \Rightarrow x = - \frac{\sqrt{3}}{2}, x = - \frac{\sqrt{3}}{2}$

Hence, $x = - \frac{\sqrt{3}}{2}, - \frac{\sqrt{3}}{2}$ .

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