If is given that the difference between the zeros of 4x 2 – 8kx + 9 is 4 and k 0. Then k = ?

Question

If is given that the difference between the zeros of 4x 2 – 8kx + 9 is 4 and k > 0. Then k = ?

Philoid · Accepted Answer

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 =