Question

If one zero of p(x)=x²-9x+k is double the other ,then find 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.