The number of natural numbers n for which the equation (x - 8)x=n(n - 10) has no real solution is equal to

Question

The number of natural numbers n for which the equation (x - 8)x=n(n - 10) has no real solution is equal to (A) 2 (B) 3 (C) 4 (D) 5

Tardigrade Admin · Accepted Answer

x2-8x-n(n - 10)=0 has no real solution. ⇒ 64+4n(n - 10) < 0 ⇒ n2-10n+16 < 0 ⇒ (n - 8)(n - 2) < 0 ⇒ 2 < n < 8 ⇒ n=3,4,5,6,7 ⇒ Number of values of n is 5

Q. The number of natural numbers $n$ for which the equation $(x - 8) x = n (n - 10)$ has no real solution is equal to

$2$

$3$

$4$

$5$

$x^{2} - 8 x - n (n - 10) = 0$ has no real solution.
$\Rightarrow 64 + 4 n (n - 10) < 0$
$\Rightarrow n^{2} - 10 n + 16 < 0$
$\Rightarrow (n - 8) (n - 2) < 0$
$\Rightarrow 2 < n < 8$
$\Rightarrow n = 3, 4, 5, 6, 7$
$\Rightarrow$ Number of values of $n$ is $5$

Q. The number of natural numbers n for which the equation (x−8)x=n(n−10) has no real solution is equal to

2

3

4

5

x2−8x−n(n−10)=0 has no real solution. ⇒64+4n(n−10)<0 ⇒n2−10n+16<0 ⇒(n−8)(n−2)<0 ⇒2<n<8 ⇒n=3,4,5,6,7 ⇒ Number of values of n is 5

Q. The number of natural numbers $n$ for which the equation $(x - 8) x = n (n - 10)$ has no real solution is equal to

$2$

$3$

$4$

$5$

$x^{2} - 8 x - n (n - 10) = 0$ has no real solution.
$\Rightarrow 64 + 4 n (n - 10) < 0$
$\Rightarrow n^{2} - 10 n + 16 < 0$
$\Rightarrow (n - 8) (n - 2) < 0$
$\Rightarrow 2 < n < 8$
$\Rightarrow n = 3, 4, 5, 6, 7$
$\Rightarrow$ Number of values of $n$ is $5$