Consider the equation x 2 + 4 x − n = 0 , where n ∈ [ 20 , 100 ] is a natural number. Then the number of all distinct values of n , for which the given equation has integral roots, is equal to

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​ x 2 + 4 x + 4 = n + 4 ( x + 2 ) 2 = n + 4 x = − 2 ± n + 4 ​ ∵ 20 ≤ n ≤ 100 24 ​ ≤ n + 4 ​ ≤ 104 ​ ⇒ n + 4 ​ ∈ { 5 , 6 , 7 , 8 , 9 , 10 } ​ ∴ ′ 6 ' integral values of ' n ' are possible

Mathematics - Quadratic Equation Question with Solution | TestHub

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