Possible Question on Intermediate Value Theorem

Asked Apr 24 '22 at 17:10

Active Apr 24 '22 at 17:10

Viewed 39 times

Let $P\left(x\right)=x^{10}+a_2x^8+a_3x^6+a_4x^4+a_2x^2$ be a polynomial with real coefficients. If P(1)=1 and P(2)=-5, then the minimum number of distinct real zeroes of P(x) is?

I think we need to solve this question using Intermediate Value Theorem, but I am not really sure how to implement that over here.

asked Apr 24 '22 at 17:10

Anonymousstriker38596

1

To see how to implement it, read for example this post. – Dietrich Burde Apr 24 '22 at 17:29
The question helped somewhat, but I am still not able to quite understand the solution. Apart from that I think that method wouldn't work on this question as when the function approaches infinity regardless of whether x approaches infinity or -ve infinity. – Anonymousstriker38596 Apr 24 '22 at 17:43
$P$ is an even function with a zero at 0, a zero in $(1,2)$ (by IVT), and one in $(2,\infty)$ ($P$ has limit $\infty$ at $\infty$). – David Mitra Apr 24 '22 at 18:01
Thanks a lot, that helped. – Anonymousstriker38596 Apr 24 '22 at 18:09

Possible Question on Intermediate Value Theorem

0 Answers0