Question

solve question number 36.

Answer 1

answer 36

p(x) = x³-3px²+qx -r

The standard form of a cubic equation is:
x³+ (a+b+c)x²+(ab+bc+ca)x+abc=0.
where a , b, c are the roots of this cubic polynomial
Comparing this equation with the given polynomial:
We find
3p = a + b + c. (1)
when a , b, c are in ap
then
let a = m - n (first term)
b = m (second term)
c = m + n ( third term)
[:. where n is the common difference]
so putting this value in first equation

3p = m-n + m + m+n
3p = 3m
p= m

compairing the coefficient of "X" in the equations
we get
q = ab + bc + ac
q = (m-n)m + m(m+n) + (m-n)(m+n)
n²=3m²-3q
n²=3p²-3q

for r
-r = (a-d)a(a+d)
putting the values ( a = m-n, b = m , c = m+n)
and the values of m and n
you'll get the answer