Question

Please help with the following problem:

The polyniomial function f(x) = 6x^3 + 19x^2 + 8x - 5 has exactly one positive zero.
Use the Intermediate Value Theorem to approximate the zero correct to 2 decimal places.

Answer 1

I got this from: http://answers.yahoo.com/question/index?qid=20090926213030AAB5kBe

here so that you don't need to find it to the link:

The polynomial function f(x) = 6x^3 + 19x^2 + 8x - 5 has exactly one positive zero. Use the Intermediate Value Theorem to approximate the zero correct to two decimal places.
It is obvious that, f(0) = -5 and f((1) = 28, so zero must lie between 0 and 1Let us find out f(1/2)
5(1/2) = 6/8+19/4+8/2 -5 = 9 - 5 = 4 Now lets us try x = 0.4
f(0.4) = 1.624 Now let us try f(0.3)
f(0.3) = -0.728 Now let us try x = 0.35
f(0.35) = 0.3875 So zero lies between o.3 and 0.35. Let us try x = 0.34
f(0.34) = 0.15224. Let us try x = 0.32
f(0.32) = -0.297792. So the zero correct totwodecimal places is
x = 0.33, f(0.33) = -0.075278 zero lies between 0.33 and 0.34

Answer 2

Thank you!