[JEE Advanced 2003] If $x^2+(a-b)x+(1-a-b)=0$ ($a,b\in\mathbb R$) has unequal real roots for all $b$, find the values of $a$.
If $x^2+(a-b)x+(1-a-b)=0$ ($a,b\in\mathbb R$) has unequal real roots for all $b$, find the values of $a$.
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· 1mo ago
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Answer: $a>1$.
Discriminant $(a-b)^2-4(1-a-b)>0$ as a quadratic in $b$ must hold for all $b$, requiring its discriminant $<0$: $32-32a<0\Rightarrow a>1$.
JEE Advanced 2003 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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