Question

Solve each equation using the quadratic formula. Find the solutions.

4x^2 - 8x + 1 = 0

Answer 1

1±√3/2

Explanation:

Given quadratic equation is :

4x²-8x+1=0

Quadratic formula is :

x=(-b±√b²-4ac)/2a

ax²+bx+c=0 is standard quadratic equation.

Comparing given equation with standard equation,we get

a=4 , b=-8 and c=1

Putting above values in quadratic formula,we get

x=(-(-8)±√(-8)²-4(4)(1))/2(4)

x=(8±√64-16)/8

x=(8±√48)/8

x=(8±√16×3)/8

x=(8±4√3)/8

x=4(2±√3)/8

x=(2±√3)/2

x=1±√3/2 is the solution of given quadratic equation.

Answer 2

Solution is : x = 1 ± 0.5√3

Explanation:

We have given quadratic equation:

4x² - 8x + 1 = 0

We need to find solution using quadratic formula.

i.e x =
`\frac{-b+(-)\sqrt{b^(2)-4ac } }{2a}`

Compare from general quadratic equation ax² + bx + c=0

Here a= 4 , b = -8 and c = 1

∴ x = -(-8)±√((-8)²-4·4·1) / 2·4

x = (8 ±√48 )/8

x = 1 ± 0.5√3 , This is the answer