Question

Q.2 How many real solution does the equation x7+14x5 +16x3 +30x - 560 = 0 have? [AIEEE-2008] (A) 1 (B)3 (C) 5 (D) 7

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

( f(x)=x+14 x^{5}+16 x^{3}+30 x-560=0 ) ( f(n)=7 x^{6}+70 x^{4}+48 x^{2}+30>0 ) it is shictly increasing [ begin{array}{l}text { when } x rightarrow infty ; f(n) rightarrow infty x rightarrow-infty ; f(n) rightarrow-inftyend{array} ] it cuts ( x ) anis at exactey one point ( therefore ) it has only one real root