Question

find the quadratic equation alpha + beta is equals to root 3 alpha beta is equals to one upon two​

Answer 1

Step-by-step explanation:

Given,

$\alpha+\beta=\sqrt3\ and\ \alpha \times \beta=\frac{1}{2}\\ \rm where\ \alpha\ and\ \beta\ are\ the\ zeroes\ of\ the\ polynomial.\\ \rm So,\ when\ the\ sum\ and\ product\ of\ zeroes\ is\ given,\ then\ we've\ to\ use\ the\ formula\\ x^2-(\alpha+\beta)x+(\alpha \times \beta)=0\\ \rm Simply\ putting\ values\ in\ the\ equation\\ \\ \rm x^2-(\sqrt3)x+(\frac{1}{2})=0\\ \\ \implies x^2-\sqrt3x+\frac{1}{2}=0\\ \\ \rm Taking\ LCM,\ we\ get\ 2\ as\ the\ common\ denominator\\ \rm Multiplying\ x^2\ and\ -\sqrt3 x\ by\ 2, we\ get\\ \\ 2x^2-2\sqrt3x+\frac{1}{2}=0\\ \\ \implies \rm 2x^2-2\sqrt3x+1=0 (\because cross-multiplying)\\ \\ \therefore \bf The\ Quadratic\ equation\ is\ 2x^2-2\sqrt3 x+1=0$