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QJEEM07Ma2f74: JEE Main 2007 Mathematics - Class 11 JEEM07Ma2f74 Solution: If the difference between the roots of the equation is less…
If the difference between the roots of the equation is less than then the set of possible values of is
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Step-by-Step Verified Solution
Let and are roots of the equation
So, and
given \left| {\alpha - \beta } \right| < \sqrt 5
\Rightarrow \sqrt {{{\left( {\alpha - \beta } \right)}^2} - 4\alpha \beta } < \sqrt 5
(as )
\Rightarrow \sqrt {{a^2} - 4} < \sqrt 5
\Rightarrow {a^2} - 4 < 5
\Rightarrow {a^2} - 9 < 0 \Rightarrow {a^2} < 9
\Rightarrow - 3 < a < 3
So, and
given \left| {\alpha - \beta } \right| < \sqrt 5
\Rightarrow \sqrt {{{\left( {\alpha - \beta } \right)}^2} - 4\alpha \beta } < \sqrt 5
(as )
\Rightarrow \sqrt {{a^2} - 4} < \sqrt 5
\Rightarrow {a^2} - 4 < 5
\Rightarrow {a^2} - 9 < 0 \Rightarrow {a^2} < 9
\Rightarrow - 3 < a < 3