SOLUTION: Use the intermediate value theorem to determine, if possible, whether g(x)=-2x^3-3x+10 has a zero between -1 and 0. If it is not possible to make a determination using this method,

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Use the intermediate value theorem to determine, if possible, whether g(x)=-2x^3-3x+10 has a zero between -1 and 0. If it is not possible to make a determination using this method,      Log On


   

Question 966543: Use the intermediate value theorem to determine, if possible, whether g(x)=-2x^3-3x+10 has a zero between -1 and 0. If it is not possible to make a determination using this method, state this.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29=-2x%5E3-3x%2B10 has a zero between -1 and 0;
find the value of g%28-1%29 and g%280%29, and see where it (if at all) changes sign, that will be the answer
g%28-1%29=-2%28-1%29%5E3-3%28-1%29%2B10
g%28-1%29=-2%28-1%29%2B3%2B10
g%28-1%29=2%2B3%2B10
g%28-1%29=15=>g%28-1%29%3E0
find the value of g%280%29
g%280%29=-2%280%29%5E3-3%280%29%2B10
g%280%29=0%2B0%2B10
g%280%29=10=>g%280%29%3E0%0D%0A%0D%0Aas+you+can+see+there+is+%7B%7B%7Bno changes in sign, so the answer is g%28x%29=-2x%5E3-3x%2B10 does not have a zero between -1 and 0
or, since g%28-1%29+%3E0 and g%280%29+%3E+0 and g is a polynomial, the Intermediate Value Theorem tells us that g%28x%29+=+0 for some value of x that is not between -1 and 0
let's see it on a graph:
+graph%28+600%2C+600%2C+-25%2C+25%2C+-25%2C25%2C+-2x%5E3-3x%2B10%29+