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

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Solution

The correct option is C 8
$x^{2} + 2 x - n = 0$

For interger roots $b^{2} - 4 a c$ should be perfect square

$4 + 4 n = p^{2}$

$4 (1 + n) = p^{2}$

$(n + 1)$ should be a square integer

$∴ n \in 8, 15, 24, 35, 48, 63, 80, 99$

So $8$ values of $n$ .

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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

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[5, 100]

, then the number of integral roots of the equation

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

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a

so that

x^{2} - x - a = 0

has integral roots, where

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and

6 \leq a \leq 100

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x^{2} + x - a = 0, a \in N

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

The correct option is C 8x2+2x−n=0For interger roots b2−4ac should be perfect square4+4n=p24(1+n)=p2(n+1) should be a square integer∴n∈8,15,24,35,48,63,80,99So 8 values of n.

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

The correct option is C 8
$x^{2} + 2 x - n = 0$

For interger roots $b^{2} - 4 a c$ should be perfect square

$4 + 4 n = p^{2}$

$4 (1 + n) = p^{2}$

$(n + 1)$ should be a square integer

$∴ n \in 8, 15, 24, 35, 48, 63, 80, 99$

So $8$ values of $n$ .