Question

If x^2 + ax + b = 0 and x^2 + bx + a = 0 have exactly 1 common root then what is the value of (a + b)?

(a) 1

(b) 0

(c) -1

(d) 3

The question was asked in an interview for job.

I would like to ask this question from Quadratic Equations in portion Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Correct answer is (c) -1

Easy explanation: Subtracting the equation x^2 + ax + b = 0 to x^2 + bx + a = 0 by solving the equation simultaneously, we get,

(a – b)x + (b – a) = 0

So, (a – b)x = (a – b)

Therefore, x = 1

Now, putting the value of x = 3 in any one of the equation, we get,

1 + a + b = 0

Therefore, a + b = -1.