If α β are roots of quadratic x 2+( k -5) x +3=0 and α

Question

If α β are roots of quadratic x 2+( k -5) x +3=0 and α<1<β and k ∈ I. If largest possible value of k is n then [ log (n2+2)(n2+n+1)] is equal to [Note: [ k ] denotes greatest integer function less than or equal to k.) (A) 0 (B) 1 (C) 2 (D) 4

Tardigrade Admin · Accepted Answer

Θ 1 lies between roots ∴ f (1)<0 1+ k -5+3< 0 ⇒ k <1 ∴ n =0 ∴ log ( n 2+2)( n 2+ n +1)=0

Q. If $α & β$ are roots of quadratic $x^{2} + (k - 5) x + 3 = 0$ and $α < 1 < β$ and $k \in I$ . If largest possible value of $k$ is $n$ then $[lo g_{(n^{2} + 2)} (n^{2} + n + 1)]$ is equal to
[Note: $[k]$ denotes greatest integer function less than or equal to $k$ .)

0

1

2

4

$Θ1$ lies between roots
$∴ f (1) < 0$
$1 + k - 5 + 3 < 0$
$\Rightarrow k < 1$
$∴ n = 0$
$∴ lo g_{(n^{2} + 2)} (n^{2} + n + 1) = 0$

Q. If α&β are roots of quadratic x2+(k−5)x+3=0 and α<1<β and k∈I. If largest possible value of k is n then [log(n2+2)​(n2+n+1)] is equal to [Note: [k] denotes greatest integer function less than or equal to k.)

0

1

2

4

Θ1 lies between roots ∴f(1)<0 1+k−5+3<0 ⇒k<1 ∴n=0 ∴log(n2+2)​(n2+n+1)=0

Q. If $α & β$ are roots of quadratic $x^{2} + (k - 5) x + 3 = 0$ and $α < 1 < β$ and $k \in I$ . If largest possible value of $k$ is $n$ then $[lo g_{(n^{2} + 2)} (n^{2} + n + 1)]$ is equal to
[Note: $[k]$ denotes greatest integer function less than or equal to $k$ .)

$Θ1$ lies between roots
$∴ f (1) < 0$
$1 + k - 5 + 3 < 0$
$\Rightarrow k < 1$
$∴ n = 0$
$∴ lo g_{(n^{2} + 2)} (n^{2} + n + 1) = 0$