Question

If the equations x² + bx - a = 0 and x²- ax +b= 0 have atleast one common root, then​

Answer 1

Now here we have two equations with exactly one common root

x^2 + ax + b = 0 and x^2 + bx + a = 0

Let y be the exact common root.

Therefore, y^2 + ay + b = 0 …..(1)

And y^2 + by + a = 0 ……..(2)

Now subtracting eq (1) from (2) we get ,

y(a - b) + (b - a) = 0

y (a - b) = - (b -a)

y (a - b) = (a - b)

y = 1

Therefore the common root is 1.

Substituting value of y in equation (1)

(1)^2 + a(1) + b = 0

1 + a + b = 0

a + b = -1

Therefore value of a + b is -1