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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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