If is given that the difference between the zeros of 4x2 – 8kx + 9 is 4 and k > 0. Then k = ?
Let us assume the zeros of the polynomial be
We have,
p (x) = 4x2 – 8kx + 9
Now comparing the given polynomial with ax2 + bx + c, we get:
a = 4, b = - 8kx + 9
Sum of roots =
=
2 + 4 = 2k
+ 2 = k
= (k – 2) (i)
, we have product of roots,
=
+ 4) =
(k – 2) (k – 2 + 4) =
(k – 2) (k + 2) =
k2 – 4 =
4k2 – 16 = 9
4k2 = 25
k2 =
k =
k =