Question

Use the quadratic formula to find the solutions to the equation.
3x^2- 10x+ 5 = 0

Answer 1

`x =(5)/(3) \pm (√(10))/(3) \\\\x=2.72076\\x=0.612574\\`

Explanation:

The quadratic equation is:

`3x^2 - 10x + 5 = 0`

The roots (solutions) of a quadratic equation of the form

`a^2 + bx + c = 0\\`

are

`x = ( -b \pm √(b^2 - 4ac))/( 2a )`

in this case we have a = 3, b = -10, and c = 5

So, substituting for a, b and c we get

`x = ( -(-10) \pm √((-10)^2 - 4(3)(5)))/( 2(3) )`

`x = ( 10 \pm √(100 - 60))/( 6 )\\`

`x = ( 10 \pm √(40))/( 6 )`

Simplifying we get

`x = ( 10 \pm 2√(10)\, )/( 6 )\\\\x = ( 10 )/( 6 ) \pm (2√(10)\, )/( 6 )\\\\x = ( 5)/( 3 ) \pm ( √(10)\, )/( 3 )\\\\( 5)/( 3 ) + ( √(10)\, )/( 3 ) = 2.72076\\\\\\` (First root/solution)

`( 5)/( 3 ) - ( √(10)\, )/( 3 ) = 0.612574` (Second root/solution)