Question

2.
If'a' and 'b’are unequal and x2 + ax + b and x2 + box + a have a common factor find
a + b.
A​

Answer 1

Answer:

nice question............

Answer 2

Let the factors of x² + ax + b = (x - α), (x - β)

And that of x² + bx + a = (x - α), (x - β).

Therefore,

for polynomial 1 (in terms of α) = α² + α·a + b __(A)

for polynomial 2 (") = α² + α·b + a __(B)

Now, subtracting B from A:-

(α² + α·a + b) - (α² + α·b + a) = 0

=> α² + α·a + b - α² - α·b - a = 0

=> (a + b)·α - (a + b) = 0

=> (a + b)·α = (a + b)

=> α = 1.

Putting α = 1 in any of the polynomial, say x² + ax + b:

1² + a·1 + b = 0

=> a + b = - 1.