Inspired by Challenge Master note (Problem is edited)

Algebra Level 3

Evaluate Ω \Omega :

Ω = ∑ − 50 49 sgn ( x 2 + 5 x + 6 ) \large \Omega = \displaystyle\sum_{-50}^{49} \text{sgn}(x^2 + 5x + 6)

Notations:

  • sgn ( x ) \text{sgn}(x) denotes the signum function of x x

  • sgn ( x ) = { 1 , x > 0 0 , x = 0 − 1 , x < 0 \text{sgn}(x) = \begin{cases} 1 \quad,\quad x>0 \\ 0 \quad,\quad x=0 \\ -1 \quad,\quad x<0 \end{cases}


The answer is 98.

Akhil Bansal by Akhil Bansal , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Tom Engelsman
Apr 5, 2018

The above quadratic expression, x 2 + 5 x + 6 = ( x + 2 ) ( x + 3 ) x^2 + 5x + 6 = (x+2)(x+3) , is zero for x = − 2 , − 3 x = -2, -3 and 1 for x ∈ [ − 50 , − 4 ] ∪ [ − 1 , 49 ] x \in [-50, -4] \cup [-1,49] . Hence, Ω = ( 2 ) ( 0 ) + ( 1 ) ( 98 ) = 98 . \Omega = (2)(0) + (1)(98) = \boxed{98}.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...