Question

If one zero of p(x) 4x² - (8k²-40k)x - 9 is negative of the other, find values
of k.

Answer 1

let the first zero be "a"
and second zero be "-a"

sum of zeroes = -b/a

a + (-a) = (8k²-40k)/4
a - a = 2k²-10k

0 = 2k²-10k

0 = 2k (k -5)

2k = 0 , k - 5 = 0
k = 0,. K = 5


hence, k = 5,0

Answer 2

Hi !

Let one zero be "x" , then the other zero is "-x"

p(x) = 4x² - (8k²-40k)x - 9 

a = 4
b = - (8k²-40k)
c = -9

sum of zeros = -b/a

x + (-x) = -(-{8k²-40k})/4

0 = 8k² - 40k/4

8k²- 40k = 0

8k² = 40k

cancelling k on both sides ,

8k = 40

k = 40/8

k = 5
----------------------------------------------------------------------------

0 = 8k² - 40k/4

0 = 2k²-10k

0 = 2k²-10k

0 = 2k (k -5)

Here ,

2k = 0 , k - 5 =0

k = 0 , k = 5

Hence,

values of k are 0 and 5