Question

find the root of each of the following equation if they exist by applying quadratic formula. <br />2x²+6root3x-60​

Answer 1

Step-by-step explanation:

2x

2

+6

3

x−60=0

Compare given equation with the general form of quadratic equation, which is ax

2

+bx+c=0

a=2,b=6

3

,c=−60

Find Discriminant:

D=b

2

−4ac

=(6

3

)

2

−4.2.−60

=108+480

=588>0

Roots of equation are real.

Find roots:

x=

2a

−b±

D

=

2×2

−6

3

±

196×3

=

2

−3

3

±7

3

Roots are :

x=2

3

and x=−5

3

Answer 2

2x² + 6√3 - 60 = x² + 3√3 - 30

x² + 3√3 - 60 = 0 ,

• a = 1

• b = 3√3

• c = -60

Applying the quadratic formula ,

• $\frac{-b±\sqrt{b²-4ac}}{2a}$

• $\red{\implies}$$\frac{-3√3±\sqrt{(3√3)²-4(-60)}}{2}$

• $\red{\implies}$$\frac{-3√3±\sqrt{(27+240)}}{2}$

• $\red{\implies}$$\frac{-3√3±\sqrt{(267)}}{2}$