Question

If a and b are roots of the equation x² + a x + b = 0, then a + b =
A. 1
B. 2
C. – 2
D. – 1

Answer 1

Answer:

The value of a + b = -1

Step-by-step explanation:

It is given that, a and b are roots of the equation x^2 + ax +b = 0.

Therefore, 1)

 a is root, a^2 + a*a + b = 0

Therefore, a^2 + a^2 + b = 0

Thus, 2a^2 + b = 0.                         eqn. 1.

 Therefore, 2)

bis root,  b^2 + ab +b = 0.       eqn 2.

Thus, eqn 1 = eqn 2.

This implies,

                      2a^2 + b= b^2 + ab + b

Thus, 2a^2 = b^2 + ab

Therefore,      2a^2 = b(b + a)

                 thus,      2a^2 /b = b+ a

But from eqn,  1:-   2a^2+ b= 0

                                     2a^2 = -b.

Replacing this we get,

                               -b/b = a + b

Therefore, -1 = a + b.

HOPE THIS HELPS YOU...