Menu Close

The-largest-interval-for-which-x-12-x-9-x-4-x-1-gt-0-is-a-4-lt-x-0-b-0-lt-x-lt-1-c-100-lt-x-lt-100-d-lt-x-lt-

Tinku Tara 0 Comments
Pin




Question Number 75013 by necxxx last updated on 05/Dec/19
The largest interval for which x^(12) −x^9 +x^4 −x+1>0 is (a)−4<x≤0 (b)0<x<1 (c)−100<x<100 (d)−∞<x<∞
Thelargestintervalforwhichx12−x9+x4−x+1>0is(a)−4<x⩽0(b)0<x<1(c)−100<x<100(d)−∞<x<∞
Answered by mind is power last updated on 05/Dec/19
let p(x)=x^(12) −x^9 +x^4 −x+1 if x<0 −x^9 >0,−x>0⇒p(x)≥1⇒p(x)>0 x>0 x^(12) −x^9 =x^9 (x^3 −1) x^4 −x=x(x^3 −1) ⇒p(x)=(x^3 −1)(x+x^9 )+1 p(x)>0,for x>1 if x∈[0,1[ 1−x>0 x^4 −x^9 ≤x^4 −x^5 =x^4 (1−x)>0 ⇒p(x)>0 ⇒∀x∈R p(x)>0
letp(x)=x12−x9+x4−x+1ifx<0−x9>0,−x>0⇒p(x)⩾1⇒p(x)>0x>0x12−x9=x9(x3−1)x4−x=x(x3−1)⇒p(x)=(x3−1)(x+x9)+1p(x)>0,forx>1ifx∈[0,1[1−x>0x4−x9⩽x4−x5=x4(1−x)>0⇒p(x)>0⇒∀x∈Rp(x)>0

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *