Question

Find the zeros of the quadratic polynomial 2x² − 11x + 15 and verify the relation between the zeros and the coefficients.

Answer 1

$\begin{array}{l}\text{We have:}\\ f\left(x\right)=2x^2-11x+15\\ =2x^2-(6x+5x)+15\\ =2x^2-6x-5x+15\\ =2x(x-3)-5(x-3)\\ =(2x-5)(x-3)\\ \therefore f\left(x\right)=0=>(2x-5)(x-3)=0\\ =>2x-5=0\text{or}x-3=0\\ =>x=\frac{5}{2}\text{or}x=3\\ \text{So, the zeroes of}f\text{(}x\text{) are}\frac{5}{2}\text{and}3.\\ \text{Sum of the zeroes}=\frac{5}{2}+3=\frac{5+6}{2}=\frac{11}{2}=\frac{-\left(\text{coefficient of}x\right)}{\left(\text{coefficient of}{x}^{\text{2}}\right)}\\ \text{Product of the zeroes =}\frac{5}{2}\times \text{3}=\frac{15}{2}=\frac{\text{constant term}}{\text{(coefficient of}{x}^{\text{2}})}\end{array}$