find the equation whose roots are x^3+qx+r=0
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Given equation, x3+qx+r=0………………(1)
a(b+c)=a(a+b+c−a)=−a2[∵sum of the roots is 0]
⟹y=−x2orx2+y=0…………..(2)
Multiplying (2) by x and subtracting from (1), we get
(q−y)x+r=0⟹x=y−qr
Substituting value of x in (2), we get
y3−2qy2+q2y+r2=0
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ab+bc+ac
=abc
-q/-r
=q/r
with solutions
is the answer
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