Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 4u² + 8u.

4u² + 8u
= 4u² +8u
= 4u(u + 2)
The value of 4u² + 8u is zero if 4u = 0 or u + 2 = 0.
⇒ u = 0 or u = -2.
Therefore, the zeroes of 4u² + 8u are 0 and -2.
Now, Sum of zeroes = 0 + (-2) = -2 = -(8)/4 = -(Coficient of u)/Cofficient of u²)
Product of zeroes = 0 x (-2) = 0 = 0/4 = (Constant term)/(Cofficient of u²)

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The study of polynomials can be beneficial to students by helping them develop important mathematical skills, understand real-world applications, prepare them for further study, and improve their problem-solving skills.