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Find the integral values of a for which the equation `x^4-(a^2-5a+6)x^2-(a^2-3a+2)=0` has only real roots |
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Answer» Correct Answer - 3 for the equation `x^(4)-(a^(2)-5a+6)x^(2)-(a^(2)-3a+2)=0` to have real root only the equation `t^(2)-(a^(2)-5a+6)t-(a^(2)-3a+2)=0` must have both roots greater then or equal to zero `(a^(2)-5a+6)^(2)+4(a^(2)-3a+2)gt0` `(a^(2)-5a+6)/(2(a))gt0=a^(2)-5a+6gt0` `(a-2)(a-3)gt0` `a in (-infty,2]cup[3,infty)` `(3)` `-(a^(2)-3a+2)gt0` `-(a^(2)-3a+3)gt0` `-(a-1)(a-2)gt0` `a in [1,2]` From 2 & 3 we have integral value of a equal to 1 and 2 which also satisfy condition 1. ltbr `a=1,2` |
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