Maths how to make situation
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Let's take an example...
f(x)=x³+3px²+3qx+r. Find the situation which must be satisfied by the coefficient of the polynomial When sum of its two zeroes is 0?
SOLN:- β+α+Y=-b/a=-(3p)/1=-3p......(1)
A.P=(2b=ac), b=β, a=α, c=Y
2β=α+Y......(2)
Substituting the value of (2) in (1)
β+2β=-3p
3β=-3p
β=-p
Now, if β is 0 of this polynomial then
f(β)=β³+3p(β)²+3qβ+r=0
Now β=-p
f(-p)=(-p)³+3p(-p)²+3q(-p)+r=0
-p³+3p³-3pq+r=0
2p³-3pq+r=0
This is the required condition.
By this way you can create condition/situation
f(x)=x³+3px²+3qx+r. Find the situation which must be satisfied by the coefficient of the polynomial When sum of its two zeroes is 0?
SOLN:- β+α+Y=-b/a=-(3p)/1=-3p......(1)
A.P=(2b=ac), b=β, a=α, c=Y
2β=α+Y......(2)
Substituting the value of (2) in (1)
β+2β=-3p
3β=-3p
β=-p
Now, if β is 0 of this polynomial then
f(β)=β³+3p(β)²+3qβ+r=0
Now β=-p
f(-p)=(-p)³+3p(-p)²+3q(-p)+r=0
-p³+3p³-3pq+r=0
2p³-3pq+r=0
This is the required condition.
By this way you can create condition/situation
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