Question

If the numerically smaller root of x^2 + mx =2 is 3 more than the other one, then find the value of m. Select one:

Answer 1

let the two roots considered be
$\alpha \: and \: 3 + \alpha$
Now, from sum of the roots expression
$\alpha + (3 + \alpha ) = - m \\ 2 \alpha + 3 = - m$
also, the product of the roots expression gives us,
$\alpha \times (3 + \alpha ) = - 2 \\ 3 \alpha + { \alpha }^{2} + 2 = 0 \\ ( \alpha + 1)( \alpha + 2) = 0$
thus the two values of alpha are,
$\alpha = - 1 \\ \alpha = - 2$
plugging values of alpha in the first equation gives us,
m = 1 and m = -1
thus,
$m = 1 \\ m = - 1$