Respuesta :
Answer:
The roots of equations are as m = [tex]\frac{-3}{2} + \frac{\sqrt{11} }{2}[/tex] And n = [tex]\frac{-3}{2} - \frac{\sqrt{11} }{2}[/tex]
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 = [tex]\frac{ - b}{a}[/tex]
And products of roots = [tex]\frac{c}{a}[/tex]
So, m + n = [tex]\frac{ - 6}{2}[/tex] = - 3
And m × n = [tex]\frac{ - 1}{2}[/tex]
Or, (m - n)² = (m + n)² - 4mn
Or, (m - n)² = (-3)² - 4 ([tex]\frac{ - 1}{2}[/tex])
Or, (m - n)² = 9 + 2 = 11
I.e m - n = [tex]\sqrt{11}[/tex]
Again m + n = - 3 And m - n = [tex]\sqrt{11}[/tex]
Solving this two equation
(m + n) + ( m - n) = - 3 + [tex]\sqrt{11}[/tex]
I.e 2 m = - 3 + [tex]\sqrt{11}[/tex]
Or, m = [tex]\frac{-3}{2} + \frac{\sqrt{11} }{2}[/tex]
Similarly n = [tex]\frac{-3}{2} - \frac{\sqrt{11} }{2}[/tex]
Hence the roots of equations are as m = [tex]\frac{-3}{2} + \frac{\sqrt{11} }{2}[/tex] And n = [tex]\frac{-3}{2} - \frac{\sqrt{11} }{2}[/tex] Answer
