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Question 1
let the zeroes be a and b
then,
sum of zeroes = a + b = 21 / 8
product of zeroes = ab = 5 / 16
then,
K( x^2 - (a+b) x + ab)
here k = 16. then,
16 x^2 -42 x + 5 Answer.
Question 2
if x = -1 then,
p (-1) = k (-1^2) -4 (-1)+K
= k-1 +4 + k
= 2k-3
2k-3 = 0
then,
k= 3/2
Question 3
here x^2 - 4 root 3 x + 3 = 0
here a =1
b = -4 root 3
c = 3
then alpha + beta = -b/a
= 4 root 3
alpha beta = 3
then value of alpha + beta - alpha beta is
4 root 3 - 3
Question 4
sorry i don't know
Question 5
using division algorithm
p(x) = q (x) + g (x) + r (x)
x^3 - 5x^2 + 6x + 4 = (x-3) × g (x) + 4
g (x) = x^3 - 5x^2 +6 x / x-3
then g (x) = x^2 + 2x
Question 6
sorry i don't know
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