Question

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

Answer 1

Answer:

The roots of  equations are as m =  $\frac{-3}{2} + \frac{\sqrt{11} }{2}$  And n =  $\frac{-3}{2} - \frac{\sqrt{11} }{2}$    

Step-by-step 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 = $\frac{ - b}{a}$

And products of roots = $\frac{c}{a}$

So, m + n = $\frac{ - 6}{2}$ = - 3

And m × n =  $\frac{ - 1}{2}$

Or, (m - n)² = (m + n)² - 4mn

Or, (m - n)² = (-3)² - 4 ($\frac{ - 1}{2}$)

Or, (m - n)² = 9 + 2 = 11

I.e m - n = $\sqrt{11}$

Again m + n = - 3    And m - n = $\sqrt{11}$

Solving this two equation

(m + n) + ( m - n) = - 3 + $\sqrt{11}$

I.e 2 m =  - 3 + $\sqrt{11}$

Or, m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$

Similarly n =  $\frac{-3}{2} - \frac{\sqrt{11} }{2}$      

Hence the roots of  equations are as m =  $\frac{-3}{2} + \frac{\sqrt{11} }{2}$  And n =  $\frac{-3}{2} - \frac{\sqrt{11} }{2}$      Answer