Question

find the roots by quadratic formula 2x²+6√3x-60=0

Answer 1

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Answer 2

To Find:

2x² + 6√3x - 60 = 0

Solution:

2x²+6√3x-60 = 0

Comparing the given equation ax² + bx + c =0

Where a = 2, b = 6√3, c = -60

The Quadratic Formula,

Discriminant D = b² - 4ac

Now, putting the values in the formula,

           D = b² - 4ac

               = (6√3)² - 4(2)(-60)

solving (6√3)² we get 108 and after multiplying 4(2)(-60) we get 480. So,

                = 180 + 480

                = 588

Now, we check if 588 is greater than or equal to 0. 588 is greater than 0.

                = 588 > 0

Hence, the roots of the equation are real.

Now, √D = √588

         √D = 14√3

The roots of α and β are given by,

   α = -b + √D/2a [substitute the values accordingly]

      = $\frac{-(-6\sqrt{3}) + 14\sqrt{3} }{2*2}$

      = $\frac{8\sqrt{3} }{4}$ [divide 8 by 4]

      = $2\sqrt{3}$

   β = -b - √D/2a

      = $\frac{-(6\sqrt{3})-14\sqrt{3} }{2*2}$

      = $\frac{-20\sqrt{3} }{4}$ [divide -20 by 4]

      = $-5\sqrt{3}$

Hence, the roots of the equation are 2√3 and -5√3.