Find the value of k for which x = 1 is a root of the equation x2 + kx + 3 = 0. Also, find the other root.
Given x = 1 is a root of the equation x2 + kx + 3 = 0 it means it satisfies the equation.
Substituting x = 1 in equation -
12 + k(1) + 3 = 0
Putting the value of k in the given equation : x2 + kx + 3 = 0
This reduced to the quadratic equation x2 - 4x + 3 = 0
Using the splitting middle term - the middle term of the general equation is divided in two such values that:
Product = a.c
For the given equation
= 1.3
= 3
And either of their sum or difference = b
= - 4
Thus the two terms are - 1 and - 3
Sum = - 1 - 3 = - 4
Product = - 1. - 3 = 3
x(x-1)-3(x-1) = 0
(x-1)(x-3) = 0
x = 1 or x = 3
Thus other root is 3.