Question

Use the quadratic formula to solve the equation 4x²-x+3=0

Answer 1

Solution of given quadratic equation,

x = [1 + 6.86i]/8 or x = [1 - 6.86i]/8

Explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given a quadratic equation, 4x²-x+3=0

To find the solution using quadratic formula

Here a = 4, b = -1 and c = 3

We have,

x = [-b ± √(b² - 4ac)]/2a

x = [--1 ± √((-1)² - 4*4*3)]/2*4

= [1 ± √(1 - 48)]/8

= [1 ± √(-47)]/8

= [1 ± 6.86i]/8

x = [1 + 6.86i]/8 or

x = [1 - 6.86i]/8

Answer 2

`x=(1+ √(47)i)/(8)` and
`x=(1 -√(47)i)/(8)`

Explanation:

Given quadratic equation is
`4x^2-x+3=0`.

Compare with
`ax^2+bx+c=0`, we get:

a=4, b=-1, c=3

Now plug these values into quadratic formula :

`x=(-b \pm √(b^2-4ac))/(2a)`

`x=(-\left(-1\right) \pm √(\left(-1\right)^2-4\left(4\right)\left(3\right)))/(2\left(4\right))`

`x=(1 \pm √(1-48))/(8)`

`x=(1 \pm √(-47))/(8)`

`x=(1 \pm √(47)i)/(8)`

Hence final answer is

`x=(1+ √(47)i)/(8)` and
`x=(1 -√(47)i)/(8)`