Question

roots of equation 3x^2-8x+9=0

Answer 1

Step-by-step explanation:

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 3

B = -8

C = -9

Accordingly, B2 - 4AC =

64 - (-108) =

172

Applying the quadratic formula :

8 ± √ 172

x = —————

6

Can √ 172 be simplified ?

Yes! The prime factorization of 172 is

2•2•43

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 172 = √ 2•2•43 =

± 2 • √ 43

√ 43 , rounded to 4 decimal digits, is 6.5574

So now we are looking at:

x = ( 8 ± 2 • 6.557 ) / 6

Two real solutions:

x =(8+√172)/6=(4+√ 43 )/3= 3.519

or:

x =(8-√172)/6=(4-√ 43 )/3= -0.852

Answer 2

Answer:

282t8

Step-by-step explanation:

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