Question

PLZ HELP 20 POINTS ANSWER ONLY IF YOU KNOW

For the given function, determine consecutive values of x between which each real zero is located.


f(x) = –14x^4 – 7x^3 – 18x^2 + 17x + 11



There are zeros between x = 2 and x = 3, x = 1 and x = 2, 0 x = –1 and x = –2, x = –1 and x = –2, x = –2 and x = –3.



There are zeros between00 x = 1 and x = 0, x = 0 and x = –100.



There is a zero between00 x = 0 and x = 1.



There is a zero between x = 0 and x = –100.

Answer 1

• [-1, 0]
• [0, 1]

Explanation:

The constant tells us f(0) = 11.

The sum of coefficients tells us f(1) = -11.

Changing the signs of odd-degree terms and summing coefficients again tells us f(-1) = -31.

There will be real roots between values of x where there is a sign change in f(x), so ...

• there is a real root between x=-1 and x=0
• there is a real root between x=0 and x=1

The x^4 term will dominate for x-values beyond -1 or 1, so these are the only intervals in which there will be real roots.