Question

What are the roots to
the equation
2x² + 6x-1=0?

Answer 1

The roots of equations are as m =
`(-3)/(2) + (√(11) )/(2)` And n =
`(-3)/(2) - (√(11) )/(2)`

Explanation:

The given quadratic equation is 2 x² + 6 x - 1 = 0

This equation is in form of a x² + b x + c = 0

Let the roots of the equation are ( m , n )

Now , sum of roots =
`( - b)/(a)`

And products of roots =
`(c)/(a)`

So, m + n =
`( - 6)/(2)` = - 3

And m × n =
`( - 1)/(2)`

Or, (m - n)² = (m + n)² - 4mn

Or, (m - n)² = (-3)² - 4 (
`( - 1)/(2)`)

Or, (m - n)² = 9 + 2 = 11

I.e m - n =
`√(11)`

Again m + n = - 3 And m - n =
`√(11)`

Solving this two equation

(m + n) + ( m - n) = - 3 +
`√(11)`

I.e 2 m = - 3 +
`√(11)`

Or, m =
`(-3)/(2) + (√(11) )/(2)`

Similarly n =
`(-3)/(2) - (√(11) )/(2)`

Hence the roots of equations are as m =
`(-3)/(2) + (√(11) )/(2)` And n =
`(-3)/(2) - (√(11) )/(2)` Answer