Given that x=2 is a root of the equation x^2 +x +m =0, find the other root and the value of m.
Given that x = 2 is a root of the equation x^2 +x +m =0. Let the other root be x = p.
This is a quadratic equation having two roots.
Hence (x-2)(x-p) = x^2 +x +m
rArr x^2-x(p+2) +2p = x^2 +x +m
Comparing the coefficients of x and the constant term, we get -(p+2) = 1
rArr p =-3
and also, m = 2p = 2*(-3)=-6.
Therefore, the other root of the equation x^2 +x +m =0 is x = -3, and the value of m is -6.
x^2 +x +m =0
factors of -6 that add to 1 are 3 and -2
the other root is -3
Given: x=2 is a root of the equation x^2+x+m=0.
Thus, substituting the value of x, in this equation, we get,
Now, substituting the value of m in the given equation, we will factorize it to get the other root.
Thus, x=-3. Thus, x=2.
Therefore, the other root of the equation is -3.