Find the zeroes of \(t^3-2t^2-15t\) and verify relations.
\(t=0,\; t=5,\; t=-3\)
Step 1: Factorise.
Take common factor: \(t(t^2 - 2t - 15)\)
Quadratic: \(t^2 - 2t - 15 = (t - 5)(t + 3)\)
So, \(t(t - 5)(t + 3)\)
Step 2: Zeroes.
\(t = 0,\; t = 5,\; t = -3\)
Step 3: Verify.
Sum = \(0 + 5 + (-3) = 2\)
= \(-a = -(-2)\)
Pairwise sum = \(0×5 + 5×(-3) + (-3)×0 = -15\)
= \(b = -15\)
Product = \(0×5×(-3) = 0\)
= \(-c = 0\)