Question

Find the roots of 2x^2 _ 6x + 3 = 0 by using Quadratic formula?

Please answer

Answer 1

Answer:

(3 ± √3)/2

Step-by-step explanation:

Hi,

If ax² + bx + c = 0 is the quadratic equation, the the roots of the above equations are given by

                                x = (-b ±√b²-4ac)/2a.

Now, in the given equation 2x² - 6x + 3 = 0, if we compare it with the general equation,

a = 2 b = -6 and c = 3.

Hence the roots of the quadratic equation would be

x = (6 ±√(36 - 4*2*3))/2*2

=> x = (6 ±√12)/4

=> x = (3 ± √3)/2

So, roots are (3 + √3)/2 and (3 - √3)/2.

Hope, it helped.

Answer 2

Answer:

x=$\frac{6+\sqrt{12 } }{4}$

x=$\frac{6-\sqrt{12 } }{4}$

Step-by-step explanation:

we know that quadratic equation can be written as

a$x^{2}$+bx+c........(1)

its roots can be written as

x=$\frac{-b+\sqrt{b^{2}-4ac } }{2a}$.......(3)

and

x=$\frac{-b-\sqrt{b^{2}-4ac } }{2a}$........(4)

we have given

2$x^{2}$-6x+3............(2)

comparing (1) and (2) we have

a=2

b=-6

c=3

now put these values in (3) and (4) one by one we have

x=$\frac{-(-6)+\sqrt{-6^{2}-4(2)(3) } }{2(2)}$

x=$\frac{6+\sqrt{12 } }{4}$

and

x=$\frac{-(-6)-\sqrt{-6^{2}-4(2)(3) } }{2(2)}$

x=$\frac{6-\sqrt{12 } }{4}$