## malibugranprix2000 one year ago solving an equation If f(x)=x^3-8x+10, show that there are values c for which f(c) equals; a)pi b)-square root of 3 c)5,000,000

1. noureddine92

a. 15.87

2. harsimran_hs4

for each part proceed this way... a) pi let there be a number c such that f(c) = pi i.e x^3 - 8x + 10 = pi x^3 -8x +10-pi = 0 all you need to show is that there is at least one real root of this equation and you are done

3. malibugranprix2000

so for b is -9.05

4. harsimran_hs4

what -9.05 ??

5. malibugranprix2000

oh I plugged something wrong. Is it, 18.66

6. harsimran_hs4

10 + sqrt(3) = 11.732 x^3 -8x +11.732 = 0 for 2nd part

7. klimenkov

$$f(x)$$ is continuous, so it can possess any value between $$f(a)$$ and $$f(b)$$. If you put $$a=-\infty$$ and $$b=\infty$$, you will have, that your polynomial can possess any value from $$\mathbb R$$. This is the proof.

8. wio

Basically, you want to use the intermediate value theorem.