When Does the Particle Pass Through the Origin?

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SUMMARY

The particle's displacement is defined by the equation x(t) = t^3 − 5t^2 + 3t − 5 for the interval 0 ≤ t ≤ 7. To determine when the particle passes through the origin, one must solve for t when x(t) = 0. The roots of this cubic equation can be found using numerical methods or graphing techniques, yielding the time at which the particle returns to the origin, accurate to two decimal places.

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5 A particle moves horizontally in a straight line according to the rule
x(t) = t^3 − 5t^2 + 3t − 5, 0 ≤ t ≤ 7
where x metres is its displacement to the right of the origin at time t seconds.
a What is the initial position of the particle?
b After how many seconds does the particle pass through the origin, correct to 2 decimal
places?

i need help on part b. could some one help me please?
thank you
 
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When it passes the origin, the displacement is 0 right? Therefore, you could say that x(t)=0 when it passes the origin. So just find the root of the equation that suits the given domain.
 

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