Find the zeroes of \(5t^2+12t+7\) and verify relations.
\(t=-1,\; t=-\dfrac{7}{5}\)
Step 1: Factorise directly.
\((5t + 7)(t + 1) = 5t^2 + 12t + 7\)
Step 2: Zeroes.
\(5t + 7 = 0 \Rightarrow t = -\dfrac{7}{5}\)
\(t + 1 = 0 \Rightarrow t = -1\)
Step 3: Verify.
Sum = \(-1 - \dfrac{7}{5} = -\dfrac{12}{5}\)
= \(-b/a = -12/5\)
Product = \((-1)(-\dfrac{7}{5}) = 7/5\)
= \(c/a = 7/5\)