Polynomial 1

Algebra Level 3

Which of the following value is possible value of $K$ such that the inequality $x^2 - 2(4K-1)x + 15K^2 - 2K- 7> 0$ is fulfilled for any real $x$ ?

1 0 7 5 3 2 4 6

1 solution

Tay Yong Qiang
May 15, 2016

Since the quadratic equation is always positive, it has no roots, i.e. discriminant is negative.

$[2(4k-1)]^2-4(15k^2-2k-7)<0$

Upon simplifying we find that $(k-4)(k-2)<0$

$\therefore 2<x<4$ , the only solution available is $\boxed{3}$

Typo: $2 < k < 4$

Hung Woei Neoh - 5 years ago