Question

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

Answer 1

Let, p(x)=2x²-5x-(2k+1)--------(1)
Also let, α be one root of (1).
Then the other root will be 2α.
α+2α=-(-5)/2
or, 3α=5/2
or, α=5/6
Again, α×2α=-(2k+1)/2
or, 2α²=-(2k+1)/2
or, -(2k+1)/2=2×(5/6)²
or, -(2k+1)=4×25/36
or, -2k-1=25/9
or, -2k=25/9+1
or, -2k=34/9
or,  k=-34/9×1/2
or, k=-17/9 Ans.

Answer 2

HOPE IT HELPS YOU ✌✌.......