Mathematics: H(x)=(x^2)+1 and k(x)=-(x^2)+4. if k(h)=0, what are the roots/solutions? a. ±i√3 b. ±i c. ±2 d. ±1 e. ±1, ±i√3

13Step-by-step explanation:The average rate of change of a function f(x) in the closed interval [ a, b ] ishere [ a, b ] = [ 3, 9 ]f(b) = f(9) = 9² + 9 - 6 = 84f(a) = f(3) = 3² + 3 - 6 = 6average rate of change = = = 13...

H(x)=(x^2)+1 and k(x)=-(x^2)+4. if k(h)=0, what - id212401795325, hayleegreenwell34

Ответ:

smithad242

31.12.2021

Mathematics

$H(x)=(x^2)+1\ \ \ \ and\ \ \ \ K(x)=-(x^2)+4. \\\\K(H)=-(H^2)+4=-(x^2+1)^2+4=4-(x^2+1)^2=\\\\.\ \ \ =2^2-(x^2+1)^2=(2-x^2-1)(2+x^2+1)=(1-x^2)(3+x^2)=\\\\.\ \ \ =(1-x)(1+x)(x^2-3\cdot i^2)=(1-x)(1+x)(x- \sqrt{3} \cdot i)(x+ \sqrt{3} \cdot i)\\\\ K(H)=0\ \ \ \ \Leftrightarrow\ \ \ (1-x)(1+x)(x- \sqrt{3} \cdot i)(x+ \sqrt{3} \cdot i)=0\\\\x=1\ \ \ \ or\ \ \ \ x=-1\ \ \ \ or\ \ \ \ x=\sqrt{3} \cdot i\ \ \ \ or\ \ \ \ x=-\sqrt{3} \cdot i\\\\Ans.\ e.$