Question

solve by quadratic formula method​

Answer 1

Answer:

Step-by-step explanation:

4x² + 4√3x + 3    can be compared to general form ax² + bx + c

on comparing, a=4 ,

                        b=4√3  and

                        c= 3

quadratic formula:  x = ( -b ±√b²-4ac )/ 2a

on putting values of a, b, c ,

                                x = ( -4√3 ± √48 - 4(4)(3) ) / 2×4

                                x =  - 4√3/8

                                x = - √3/2

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Answer 2

GIVEN :-

$\\ \sf \: 4 {x}^{2} + 4\sqrt{3} x + 3$

TO FIND :-

• Roots of the equation by quadratic formula.

TO KNOW :-

$\\ \bigstar \boxed{\sf \: roots = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a}}$

Here ,

• a → Coefficient of x².
• b → Coefficient of x.
• c → constant.

SOLUTION :-

We have ,

$\\ \sf \: 4 {x}^{2} + 4 \sqrt{3} x + 3$

Here ,

• a = 4
• b = 4√3
• c = 3

Putting values in formula ,

$\\ \sf \: roots = \frac{ - 4 \sqrt{3} ± \: \sqrt{ {(4 \sqrt{3}) }^{2} - 4(4)(3) } }{2(4)} \\ \\ \\ \implies \sf \: \frac{ - 4 \sqrt{3} ± \sqrt{48 - 48} }{8} \\ \\ \\ \sf \implies \frac{ - 4 \sqrt{3} ± \sqrt{0} }{8}$

Discriminant is 0 . Hence , roots are equal.

$\\ \implies \sf \: \frac{ - 4 \sqrt{3} }{8} \: \: \: , \: \: \frac{ - 4 \sqrt{3} }{8} \\ \\ \\ \implies \boxed{\sf \: \frac{ - \sqrt{3} }{2} \: \: \: , \: \: \frac{ - \sqrt{3} }{2} }$

Hence , roots are -√3/2 , -√3/2.

TO CHECK :-

$\\ \sf \: 4 {x}^{2} + 4 \sqrt{3}x + 3 = 0\\ \\ \sf \implies \: 4 {\left( \frac{ - \sqrt{3} }{2} \right)}^{2} + 4 \sqrt{3} \left( \frac{ - \sqrt{3} }{2} \right) + 3 = 0 \\ \\ \\ \implies \sf \: \cancel{4}\left( \frac{3}{ \cancel{4}} \right) - \cancel\frac{12}{2} + 3 = 0 \\ \\ \\ \implies \sf \: 3 - 6 + 3 = 0 \\ \\ \\ \implies \sf \: 0 = 0 \: \: \: \: \: (verified)$