Question-123265

Question Number 123265 by Study last updated on 24/Nov/20

Commented by Study last updated on 24/Nov/20

w h i c h i s a p o l y n o m i a l ? w h y ?

Commented by mathmax by abdo last updated on 24/Nov/20

3) p (x) = \sqrt{3} is apolynom (csnstant)

Answered by MJS_new last updated on 24/Nov/20

1)

x < 0 : p (x) = i \sqrt{- x} \times i \sqrt{- x} = i^{2} \sqrt{(- x) (- x)} = - x

x ⩾ 0 : p (x) = x

\Rightarrow p (x) =∣ x ∣

2)

p (x) =∣ x ∣

3)

p (x) = \sqrt{3}

a polynome of degree n usually is defined as

p (x) = \underset{j = 0}{\sum^{n}} c_{j} x^{j} with c_{j} \in C

\Rightarrow only p (x) = \sqrt{3} is a polynome; its degree is 0

Answered by mathmax by abdo last updated on 24/Nov/20

2) p (x) = \sqrt{x^{2}} =∣ x ∣ is not polynomial

let suppose it p^{2} (x) = x^{2} \Rightarrow degp = 1 \Rightarrow p (x) = ax + b

p (1) = 1 = a + b and p (- 1) = 1 = - a + b \Rightarrow {\begin{cases} a + b = 1 \\ - a + b = 1 \Rightarrow \end{cases}

b = 1 \Rightarrow a = 0 \Rightarrow p (x) = 1 ? impossible p is not constant \dots!

Commented by mathmax by abdo last updated on 24/Nov/20

1) p (x) = x with x ⩾ 0 is not polynom