The set of real parameter ' a ' for which the equation x 4 − 2 a x 2 + x + a 2 − a = 0 has all real solutions, is given by [ n m , ∞ ) where m and n are relatively prime positive integers,

Question

The set of real parameter ' a ' for which the equation x 4 − 2 a x 2 + x + a 2 − a = 0 has all real solutions, is given by [ n m ​ , ∞ ) where m and n are relatively prime positive integers, then the value of ( m + n ) is

TestHub · Accepted Answer

We have a 2 − ( 2 x 2 + 1 ) a + x 4 + x = 0 ∴ a = 2 ( 2 x 2 + 1 ) ± ( 2 x 2 + 1 ) 2 − 4 ( x 4 + x ) ​ ​ 2 a = ( 2 x 2 + 1 ) ± ( 2 x − 1 ) On solving +ve \& -ve sign we got a ≥ 4 3 ​ ∴ m + n = 7

Mathematics - Quadratic Equation Question with Solution | TestHub

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