How do you solve 8x^2-6x+1=0?

2 Answers
Mar 30, 2017

x=1/4 or x=1/2

Explanation:

Factorise the quadratic trinomial and then let each factor be equal to 0.

8x^2-6x +1 =0

(Find factors of 8 which add up 6.)

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

If 4x-1=0" " rarr 4x=1" "rarr x =1/4

If 2x-1=0" "rarr2x=1" "rarrx=1/2

Mar 31, 2017

x= 1/2 or x = 1/4 (You usually solve equations of this type using the discriminant)

Explanation:

In any equation with the form of: ax^2 + bx + c = 0 you can calculate the discriminant ( D or Δ) by using the formula:

D = b^2 - 4 * ac

Then, there are three different cases of finding the roots depending on the discriminant

No1: if D < 0 then the equation has no rootes

No2: if D = 0 then the equation has one answer which you can find using
x = - ( b / (2*a))

No3: if D>0 then the equation has two roots which you can find using

x = ( -b +- sqrtD ) / ( 2 * a )

Let's take your example:
8x^2 - 6x + 1 = 0

D= 36 - 32 = 4 D>0

x1= (6 + 2) / 16
x1= 1 / 2

And
x2= ( 6 - 2) / 16
x2= 1 / 4