How to find m in x^-5x+m=0 x1=2x2 (this is not 2 times 2) using vieta's formulas?
Apply Vieta's formulas to a quadratic equation `ax^2 + bx + c = 0` :
`x_1 + x_2 = -b/a`
`` `x_1*x_2 = c/a`
Compare the standard quadratic equation with your equation and find coefficients a = 1, b=-5 and c=m.
Write Vieta's formulas:
`x_1 + x_2 = 5`
`` `x_1*x_2 = m`
Use the relation between roots:`x_1 = 2x_2`
`x_1 + x_2` = 5 <=> `2x_2 + x_2 ` = `3x_2 = 5` => `x_2 = 5/3` => `x_1 = 10/3`
`x_1*x_2 ` = m => `(10/3)*(5/3)` = m => m = `50/9`
The value of m is m = `50/9` .