if α, β are the roots of the quadratic polynomial p(x) = x2-(k-6)x+2(2k-1) Find the value of k,ifα+β = 1/2αβ - Maths - Polynomials

Question

if α, β are the roots of the quadratic polynomial
p(x) = x2-(k-6)x+2(2k-1) Find the value of
k,ifα+β = 1/2αβ

The Silent Guy · Accepted Answer

p(x) = x2 - (k + 6)x + 2(2k - 1)
Here a = 1, b = -(k + 6) and c = 2(2k - 1)
α + β = -b/a = -[-(k + 6)]/1 = k + 6
αβ = c/a = 2(2k - 1)/1 = 2(2k - 1)
Given,
α + β = 1/2* αβ
Putting the respective values of α + β and
αβ, we have
k + 6 = 1/2*2(2k - 1)
k + 6 = 2k - 1
k = 7
So, value of k = 7

if α, β are the roots of the quadratic polynomial p(x) = x2-(k-6)x+2(2k-1).Find the value of k,ifα+β = 1/2αβ.

if α, β are the roots of the quadratic polynomial p(x) = x²-(k-6)x+2(2k-1).Find the value of k,ifα+β = 1/2αβ.