Question

Find the zeros of the quadratic polynomial (x² + 3x − 10) and verify the relation between its zeros and coefficients.

Answer 1

$\begin{array}{l}\text{We have:}\\ f\left(x\right)=x^2+3x-10\\ =x^2+5x-2x-10\\ =x(x+5)-2(x+5)\\ =(x-2)(x+5)\\ \therefore f\left(x\right)=0=>(x-2)(x+5)=0\\ =>x-2=0\text{or}x+5=0\\ =>x=2\text{or}x=-5\\ \text{So, the zeroes of}f\text{(}x\text{)are 2 and}-\text{5}\text{.}\\ \text{Sum of the zeroes}=\text{2+(}-\text{5)}=-\text{3}=\frac{-3}{1}=\frac{-\left(\text{coefficient of}x\right)}{\left(\text{coefficient of}{x}^{\text{2}}\right)}\\ \text{Product of the zeroes= 2× (}-\text{5) =}-\text{10 =}\frac{-10}{1}=\frac{\text{constant term}}{\text{(coefficient of}{x}^{\text{2}})}\end{array}$