Question

find the condition that the zeroes of x³-px²+qx-r ,given that the zeroes are in A.P.​

Answer 1

$\huge \mathfrak{hello \: mate}$

Let a-d, a and a+d be the zeroes of the given polynomial.

Now,

Sum of the zeroes, a-d+a+a+d=-b/a

➡a-d+a+a+d=-(-p)

➡3a=p

➡a=p/3

Since, a is a zero of the given polynomial,

p(a)=0

➡a³-pa²+qa+r=0

Substituting the value of a,

➡(p/3)²-p(p/3)²+q(p/3)+r=0

➡p³/27-p³/9+pq/3+r=0

➡p³/27-3p³+9pq/27+r=0

➡p³-3p³+9pq-27r=0

➡-2p³+9pq-27r=0

➡2p³-9pq+27r=0--------The required condition