Question

Find the roots of 2x²-x✓3-3=0 using quadratic formula

Answer 1

Given p(x)=2x²-x✓3-3=0

By using Quadratic Equation

=>x= [ -(-✓3)±(✓(-✓3)^2-(4)(2)(-3)]/2*2

=>x=[ ✓3±(✓3+24)]/4

=>x=( ✓3±3✓3)/4

So, x=✓3, -✓3/2

Answer 2

HELLO DEAR,

GIVEN:-

2x² - √3x - 3 = 0

where, a = 2 , b = -√3 , c = -3

we know,

D = b² - 4ac

D = (-√3)² - 4(2)(-3)

D = 3 + 24

D = 27

now,

the quadratic formula is;

$\bold{x = \frac{-b ± \sqrt{b^2 - 4ac}}{2a}}$

$\bold{\Rightarrow x = \frac{-(-\sqrt{3}) ± \sqrt{27}}{2(2)}}$

$\bold{\Rightarrow x = \frac{\sqrt{3} ± 3\sqrt{3}}{4}}$

$\boxed{\bold{taking - sign}}$

$\bold{\Rightarrow x= \frac{-2\sqrt{3}}{4}}$

$\bold{\Rightarrow x= \frac{-\sqrt{3}}{2}}$

$\boxed{\bold{taking + sign}}$

$\bold{\Rightarrow x= \frac{4\sqrt{3}}{4}}$

$\bold{\Rightarrow x= \sqrt{3}}$

I HOPE ITS HELP YOU DEAR,

THANKS