Consider the equation $x^{2} + 2 x - n = 0$ , where $n \in N$ are $n \in [5, 100]$ .
Total number of different values of $n$ so that the given equation has integral roots is

8

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3

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6

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2

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Solution

The correct option is A $8$
$x^{2} + 2 x - n = 0 f o r i n t e g r a l r o o t s b^{2} + 4 n s h o u l d b e a p e r f e c t s q u a r e ∴ 4 + 4 n = p^{2} p^{2} = 4 (1 + n) ∴ 1 + n s h o u l d b e a p e r f e c t s q u a r e ∴ n = 8, 15, 24, 35, 48, 63, 80, 99 s o 8 v a l u e s o f n$

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Similar questions

Consider the equation $x^{2} + 2 x - n = 0$ , where n $\in$ [5,100]. Total number of different values of 'n' so that the given equation has integral roots is

Q. If

n

is a positive integer and

n \in [5, 100]

, then the number of integral roots of the equation

x^{2} + 2 x - n = 0

are:

Q. If

n

is a integer which lies in

[5, 100]

, then the number of integral roots of the equation

x^{2} + 2 x - n = 0

Q. Total number of values of

a

so that

x^{2} - x - a = 0

has integral roots, where

a \in N

and

6 \leq a \leq 100

, is equal to

Total number of values of 'a' so that $x^{2}$ - x - a = 0 has integral roots, $a ϵ N$ & 5 < a < 99 is

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Consider the equation x2+2x−n=0, where n∈N are n∈[5,100]. Total number of different values of n so that the given equation has integral roots is

The correct option is A 8x2+2x−n=0forintegralrootsb2+4nshouldbeaperfectsquare∴4+4n=p2p2=4(1+n)∴1+nshouldbeaperfectsquare∴n=8,15,24,35,48,63,80,99so8valuesofn

Consider the equation $x^{2} + 2 x - n = 0$ , where $n \in N$ are $n \in [5, 100]$ .
Total number of different values of $n$ so that the given equation has integral roots is

The correct option is A $8$
$x^{2} + 2 x - n = 0 f o r i n t e g r a l r o o t s b^{2} + 4 n s h o u l d b e a p e r f e c t s q u a r e ∴ 4 + 4 n = p^{2} p^{2} = 4 (1 + n) ∴ 1 + n s h o u l d b e a p e r f e c t s q u a r e ∴ n = 8, 15, 24, 35, 48, 63, 80, 99 s o 8 v a l u e s o f n$