Question

find the quadratic equation alpha + beta is equal to 5 Alpha Beta is equals to one upon three​

Answer 1

hence
$\alpha + \beta = - \frac{b}{a} = \frac{5}{1} \times \frac{3}{3} = \frac{15}{3}$
and
$\alpha \beta = \frac{c}{a} = \frac{1}{3}$
so the quadratic equation
${ax}^{2} + bx + c = 0$
will be
${3x}^{2} - 15x + 1 = 0$
hope it helps to you

Answer 2

Step-by-step explanation:

Given

$\rm \alpha+\beta=5\ and\ \alpha \times \beta=\frac{1}{3}\ where\ \alpha\ and\ \beta\ are\ the\ two\ zeros\ of\ the\ polynomial\\ \\ \rm Now,\ we\ know\ that\ when\ sum\ and\ product\ of\ zeroes\ is\ given,\ then\ we've\ to\ use\ this\ formula\\ \rm x^2-(\alpha+\beta)x+(\alpha \times \beta)=0\\ \rm Putting\ values\ in\ the\ formula\\ x^2-(5)x+(\frac{1}{3})=0\\ \\ \rm Taking\ LCM\ of\ the\ denominators\\ \rm The\ common\ denominator\ will\ be\ 3.\ Now\ multiply\ x^2\ and\ -5\ by\ 3\\ \rm The\ equation\ will\ be\ \frac{3x^2-15x+1}{3}=0\\ \\ \implies \rm 3x^2-15x+1=0\qquad (\because cross- multiplying)\\ \\ \therefore \rm The\ Quadratic\ equation\ is\ \bf 3x^2-15x+1=0$