Question

If the equations x2 + 4x + 5 = 0 and ax2 + bx + c = 0 have a common root, (where a, b, c e n), then e least value of a + b + c is equal to

Answer 1

Solution:

Given equation = x^2 + 4x + 5 = 0

X = - 4 + √ 16 - 20 / 2 = ( - 2 )

Find (a + b + c) = ?

Here,

* One root is Complex so other zeros obviously its conjugate as [ b^2 - 4ac < 0 ].

* So, the equation have both roots in common and as a, b and c have no common factor.

Thus, a + b + c = 1 + 4 + 5 = 10

Thus, the least value of a + b + c is equal to "10".