Question

g Given the equation: ee−xx2 (1 + 7xx4) = 1 (i) How many roots does the equation have? (ii) Plot the function over a range of x values to show those roots. (iii) Use the bisection method to find the roots.

Answer 1

Answer:

Step-by-step explanation:

(i) We have that

$e^{-x^2(1+7x^4)}=1\\ln[e^{-x^2(1+7x^4)}]=ln(1)\\-x^2(1+7x^4)=0\\x_{1,2}=0\\x_{3,4,5,6}=\pm \frac{i}{\sqrt{7}}$

Hence, there are six roots, two real and four imaginary roots

(ii)

hope this helps!!