Let p(x) be a polynomial with real co-efficients, p(0)=1 and p prime(x)0 for all x ∈ C. Then

Question

Let p(x) be a polynomial with real co-efficients, p(0)=1 and p prime(x)>0 for all x ∈ C. Then (A) p(x) has at least two real roots (B) p(x) has only one positive real root (C) p(x) may have negative real root (D) p(x) has infinitely many real roots

Tardigrade Admin · Accepted Answer

P(x)=0 has exactly one negative real root.

Q. Let $p (x)$ be a polynomial with real co-efficients, $p (0) = 1$ and $p^{'} (x) > 0$ for all $x \in C$ . Then

$p (x)$ has at least two real roots

$p (x)$ has only one positive real root

$p (x)$ may have negative real root

$p (x)$ has infinitely many real roots

$P (x) = 0$ has exactly one negative real root.

Q. Let p(x) be a polynomial with real co-efficients, p(0)=1 and p′(x)>0 for all x∈C. Then

p(x) has at least two real roots

p(x) has only one positive real root

p(x) may have negative real root

p(x) has infinitely many real roots