Question

Find condition which must be satisfied by coefficient of polynomial xcube-px square+qr-r when sum of its 2 zero iszero

Answer 1

Hello...

Please refer to this answer.

Hope it helps you!!!

If it really does, please mark as brainliest!!!

Answer 2

Answer:

Required condition:

Required condition:pq = r

Step-by-step explanation:

Let p(x) = x³-px²+qx-r,

$\alpha,\beta\: and \:\gamma\\ are \: three \: zeroes \:of \: p(x)$

$\alpha+ \beta = 0 ---(1)$\*given*\

Compare p(x) with ax³+bx²+cx+d , we get

a=1 , b=-p,c=q,d=-r

Now,

$i) \alpha+\beta+\gamma=\frac{-b}{a}$

$\implies 0+\gamma=\frac{-(-p)}{1}$

\* From (1)*\

$\implies \gamma = p--(2)$

$ii)\alpha\beta+\beta\gamma+\gamma\alpha=\frac{c}{a}$

$\alpha\beta+\gamma(\alpha+(\beta)=\frac{c}{a}$

$\implies \alpha\beta+\gamma \times 0=\frac{q}{1}$

$\implies \alpha\beta=q--(3)$

$iii) \alpha\beta\gamma=\frac{-d}{a}$

$\implies (\alpha\beta)\gamma=\frac{-(-r)}{1}$

$\implies q\times p = r$

/* From (2) and (3)

$\implies pq = r$

Therefore,.

Required condition:

pq = r

•••♪