Question

7x2 – 6x - 4 =0 has how many roots

Answer 1

Answer:

Solve Quadratic Equation using the Quadratic Formula

4.3 Solving -7x2-6x+4 = 0 by the Quadratic Formula .

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 = -7

B = -6

C = 4

Accordingly, B2 - 4AC =

36 - (-112) =

148

Applying the quadratic formula :

6 ± √ 148

x = —————

-14

Can √ 148 be simplified ?

Yes! The prime factorization of 148 is

2•2•37

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).

√ 148 = √ 2•2•37 =

± 2 • √ 37

√ 37 , rounded to 4 decimal digits, is 6.0828

So now we are looking at:

x = ( 6 ± 2 • 6.083 ) / -14

Two real solutions:

x =(6+√148)/-14=3/-7-1/7√ 37 = -1.298

or:

x =(6-√148)/-14=3/-7+1/7√ 37 = 0.440