Question

Q14
plz solve it fast if m and n are zeroes ​

Answer 1

put x=n in the equation

n^2 -(k-6)n +2(2k-1) = 0

n^2 -nk + 6n +4k -2 =0. -----(1)

put x = m

m^2 -(k-6)m +2(2k-1) =0

m^2 -mk +6m +4k -2 =0-------(2)

now , adding equation (1) & (2)

m^2 - mk +6m + 4k -2 +n^2 -nk +6n +4k-2 =0

m^2 + n^2 +6(m+n) -k(m+n) + 8k - 4 =0----(3)

as it is given , m+n=1/2

on squaring both sides ,

m^2+n^2+2mn=1/4

m^2 + n^2 = 1/4 - 2mn

put the value of (m^2 +n^2) & (m+n) in eq 3

1/4 - 2mn + 6(1/2) - k(1/2) + 8k - 4 =0

1/4 - 2mn + 3 - k/2 + 8k - 4 =0

1/4 - 1 + 15k/2 - 2mn = 0

15k/2 = 2mn +3/4

k = (2mn +3/4)×2/15

k ={ (8mn + 3)/4 }2/15

k = ( 8mn + 3 )/ 30