Determine the three zeros correct to two decimal places.

Question

A function f is given by the expression f(x)= -2x³+3x²+180x for -10 ≤ x ≤ 11

Determine the three zeroes correct to two decimal places.

Answer 1

x=0 is one zero, as f(0) = 0

that leaves -2x^2 +3x + 180= 0

use the quadratic formula, if you can't factor it

x = 3/4 + or - (1/4)sqr(9+8(180))

x = 3/4 + or - about 38.1/4 = .75 + or - 9.52

x = 10.27 or -8.77

the three zeros are -8.77, 0.00, and 10.27 rounded to two decimal places

0 is exactly a zero, not rounded

-2(10.27)^3 +3(10.27)^2 + 180(10.27) = about 0

-2(0)^3 +3(0)^2 + 180(0) = exactly 0

-2(-8.77)^3 +3(-8.77)^2 + 180(-8.77) = about 0