Question

Find the zeros of the quadratic polynomial (5u² + 10u) and verify the relation between the zeros and the coefficients.

Answer 1

$\begin{array}{l}\text{We have:}\\ f\left(u\right)=5u^2+10u\\ \text{It can be written as 5}\mathit{\text{u}}\text{(}u+2)\\ \therefore f\left(u\right)=0=>5u=0oru+2=0\\ =>u=0\text{or}\mathit{\text{u}}\text{=-2}\\ \\ \text{So, the zeroes of}f\text{(}u\text{) are}-\text{2 and 0}\text{.}\\ \text{Sum of the zeroes}=-\text{2+ 0=}-\text{2}=\frac{-2\times 5}{1\times 5}=\frac{-10}{5}=\frac{-\left(\text{coefficient of}u\right)}{\left(\text{coefficient of}{u}^{\text{2}}\right)}\\ \text{Product of the zeroes=}-\text{2}\times \text{0}=0=\frac{0\times 5}{1\times 5}=\frac{0}{5}=\frac{\text{constant term}}{\text{(coefficient of}{u}^{\text{2}})}\end{array}$