Question

Respected Sir,

Please help me in solving my below mentioned doubt,

If a + b + c = 0, then find one of the roots of quadratic equation ax² + bx + c = 0

Answer 1

method I

Here, we have,
x = [-b +/- sqrt(b^2 - 4ac)] / 2a ................... [1]
Since,
a+b+c = 0 ==> b = -(a+c)
b^2 = (a+c)^2 = a^2+c^2 +2ac

b^2 -4ac = a^2+c^2-2ac = (a-c)^2 ........... [2]

From [1] and [2], we get,
x = [(a+c) +/- (a-c)] / 2a = 2a/2a or 2c/2a

x = 1 , and x = c/a

method II
by trial and error method we get
P(x ) = ax² + bx + c
put x = 1

P(1) = a + b + c
but a + b + c = 0
so, P(1) = 0
so, x = 1 is the root of P(x )