Question

if one zero of polynomial 2 x^2 - 5x -( 2 k + 1 )is twice the Other ,find both the zeroes of the polynomial and the value of k​

Answer 1

Answer:

Let, p(x)=2x^2-5x-(2k+1)--------(1)Also let, α be one root of (1).Then the other root will be 2α.α+2α=-(-5)/2or, 3α=5/2or,α=5/6Again,α + 2α=-(2k+1)/2or, 2α^2=-(2k+1)/2or, -(2k+1)/2=2x(5/6)^2or, -(2k+1)=4x25/36or, -2k-1=25/9or, -2k=25/9+1or, -2k=34/9or, k=-34/9 x 1/2or, k=-17/9 Ans.