Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let a be an integer such that all real roots the polynomial  l

Let a be an integer such that all real roots the polynomial 2x^2 +5x^4+10x^3+10x^2+10x+10 lie in the interval (a,a+1). Then, \left | a \right | is equal to ____
Option: 1 2
Option: 2 4
Option: 3 6
Option: 4 5

Answers (1)

best_answer

\\\text { Let } 2 x^{5}+5 x^{4}+10 x^{3}+10 x^{2}+10 x+10=f(x) \\f(x)=x^{5}+x^{5}+5 x^{4}+10 x^{3}+10 x^{2}+5 x+10+5 x+9 \\ f(x)=x^{5}+5 x+9+(x+1)^{5}\\f'(x)=5x^4+5+0+5(x+1)^4>0\\\text{f(x) is an increasing function}

\begin{aligned} &\text { Now } f(-2)=-34 \text { and } f(-1)=3\\ &\text { Hence } f(x) \text { has a root in }(-2,-1) \end{aligned}

So, a = -2, |a| = 2.

Posted by

himanshu.meshram

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Advanced 2024: Chemical engineering cut-offs at IITs; know opening, closing ranks
anam-khan

IIT JEE Mains Result 2024 Session 2: How is overall merit list prepared?
anam-khan

JEE Mains Session 2 result 2024 soon; List of top NITs in India

Latest Question