Question

Find the roots of 4x^2 - 5x = 3? In simplest radical form.

Answer 1

Use the formula `x_1,2=(-b(+or-)(b^2-4*a*c)^(1/2))/(2*a)`

Explanation:

Write the equation in form:`ax^2+bx+c=0`
`4x^2-5x-3=0`
Apply the formula:
`x_1=(5+(5^2-4*4*(-3))^(1/2))/(2*4)=(5+(25+16*3)^(1/2))/(8)= (5+(25+16*3)^(1/2))/(2*4)=(5+(73)^(1/2))/(8)`
`x_2=(5-(5^2-4*4*(-3))^(1/2))/(2*4)=(5-(25+16*3)^(1/2))/(8)= (5+(25+16*3)^(1/2))/(2*4)=(5-(73)^(1/2))/(8)`
`4x^2-5x-3=(x-(5+(73)^(1/2))/(8))(x-(5-(73)^(1/2))/(8))`

Answer 2

`x=5/8+-1/8sqrt73`

Explanation:

`"first rearrange the equation into standard form"`

`rArr4x^2-5x-3=0larrcolor(blue)"in standard form"`

`"solve for x using the "color(blue)"quadratic formula"`

`•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)larrcolor(blue)"quadratic formula"`

`"here "a=4, b=-5" and "c=-3`

`x=(5+-sqrt(25+48))/8`

`color(white)(x)=(5+-sqrt73)/8`

`rArrx=5/8+-1/8sqrt73`