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JEE Main20254 Apr 2025Morning ShiftMathematicsQuadratic EquationActual

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

Options

A7
B8
C6
D5

Correct answer

C. 6

Step-by-step solution

aligned & 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 aligned ' 6 ' integral values of ' n ' are possible

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