Question

The product of the roots of 8x^2 - 2x = 1 is:
-1/8
1/8
1/4

Answer 1

Option A. -1/8 is the correct option.

Explanation:

We have to get the product of the roots of the given equation.

Since the equation is 8x²- 2x = 1

8x² - 2x - 1 = 0

8x² - 4x + 2x -1 = 0

4x(2x - 1) + 1(2x -1) = 0

(4x + 1)(2x - 1) = 0

Here the equation has two roots

4x +1 = 0

4x = -1

x = -1/4

and 2x - 1 = 0

2x = 1

x = 1/2

Therefore product of the given roots will be

= (-1/4)×(1/2) = -1/8

Option A. -1/8 is the answer.

Answer 2

Answer: FIRST OPTION.

Explanation:

You can find the roots as following:

-Make the equation equal to zero:

`8x^(2)-2x-1=0`

- Apply the quadratic formula as following:

`x=(-b+/-√(b^2-4ac))/(2a)`

Where:

a=8

b=-2

c=-1

Therefore, you obtain:

`x=(-(-2)+/-√((-2)^2-4(8)(-1)))/(2(8))`

`x=1/2\\x=-1/4`

The product is the result of multiply both roots:

`(1/2)(-1/4)=-1/8`