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`        If p+iq is the root of the eqn x^3+ax+b=0, then eqn whose one of the roots is 2p is?`
5 months ago

```							It is given that, p+i q , is one of the roots of the equation        x³+ a x +b=0This is a cubic equation.So, it has three roots.As,Imaginary root occur in pairs. So, if , p + i q,is one root of the equation , then , p - i q, will be another root.It is given that third Root is equal to 2 p.For, any Cubic equation of the form   If, u,v and w are roots of the equation    Then, ⇒⇒p+i q + p- i q + 2 p=0         4 p=0p=0orAlso,⇒ (p +i q)(p-i q)×2 p= -b ⇒(p²+q²)×2 p= -b⇒2 p³+2 p q² + b=0or⇒(p+ i q)× (p -i q) + 2 p× ( p + i q)+2 p×(p- i q)=a⇒p²+q²+2 p²+2 p i q+2 p² -2 p i q=a⇒ 5 p² +q²-a=0
```
5 months ago
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