Question

If ‘a’ and ‘b’ are unequal and x² + ax + b and x² + bx + a have a common factor, then a + b = ……………

A) -1

B) 1 

C) 0 

D) 2

Answer 1

Correct option is (A) -1

Let the common root be \(\alpha.\)

\(\therefore\alpha^2+a\alpha+b=0\) and \(\alpha^2+b\alpha+a=0\)

\(\Rightarrow\) \((\alpha^2+a\alpha+b)\) \(-(\alpha^2+b\alpha+a)=0\)

\(\Rightarrow\) \((a-b)\alpha+b-a=0\)

\(\Rightarrow\) \(\alpha=\frac{-(b-a)}{a-b}=\frac{a-b}{a-b}=1\)

Thus, 1 is a zero of \(x^2 + ax + b.\)

\(\therefore\) 1+a+b = 0

\(\Rightarrow\) a+b = -1

Answer 2

Correct option is A) -1