alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS URGENT)

Accepted Solution

Answer:[tex]k=\frac{-11}{2}[/tex].Step-by-step explanation:We are given [tex]\alpha[/tex] and [tex]\beta[/tex] are zeros of the polynomial [tex]x^2-(k+6)x+2(2k-1)[/tex].We want to find the value of [tex]k[/tex] if [tex]\alpha+\beta=\frac{1}{2}[/tex].Lets use veita's formula. By that formula we have the following equations:[tex]\alpha+\beta=\frac{-(-(k+6))}{1}[/tex] Β (-b/a where the quadratic is ax^2+bx+c)[tex]\alpha \cdot \beta=\frac{2(2k-1)}{1}[/tex] (c/a)Let's simplify those equations:[tex]\alpha+\beta=k+6[/tex][tex]\alpha \cdot \beta=4k-2[/tex] If [tex]\alpha+\beta=k+6[/tex] and [tex]\alpha+\beta=\frac{1}{2}[/tex], then [tex]k+6=\frac{1}{2}[/tex].Let's solve this for k:Subtract 6 on both sides:[tex]k=\frac{1}{2}-6[/tex]Find a common denominator:[tex]k=\frac{1}{2}-\frac{12}{2}[/tex]Simplify:[tex]k=\frac{-11}{2}[/tex].