Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

4u² + 8u

Answer 1

4u² + 8u = 4u(u + 2)

= 4[u - 0][u - (-2)]

For p(u) = 0, we have

Either 4u = 0

u = -2

∴ The zeroes of 4u² + 8u are 0 and -2.

Relationship between the zeroes and the coefficients of the polynomial

Sum of the zeroes = `-("Coefficient of " u)/("Coefficient of " u^2)`

= `0 + (-2) =(-(8))/4`

= -2 = -2

Also product of the zeroes = `"Constant term"/("Coefficient of " u^2)`

= `0 xx (-2) = 0/4`

= 0 = 0

Thus, the relationship between the zeroes and the coefficients in the polynomial 4u² + 8u is verified.