1.

If one root of the two quadratic equations x2 + ax + b = 0 and x2 + bx + a = 0 is common, then A) a + b = -1 B) ab = -1 C) ab = 1 D) a + b = 1

Answer»

Correct option is (A) a + b = -1

Let \(\alpha\) be common root of given quadratic equations.

\(\therefore\alpha^2+a\alpha+b=0\)        ______________(1)

\(\alpha^2+b\alpha+a=0\)        ______________(2)

Subtract equation (2) from (1), we get

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

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

\(\Rightarrow(a-b)\alpha-(a-b)=0\)

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

Hence, x = 1 is a common root of given quadratic equations.

Put x = 1 in given equation, we get

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

\(\Rightarrow\) 1+a+b = 0

\(\Rightarrow\) a + b = -1

Correct option is A) a + b = -1



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