Question

3. If alpha, beta and gemma are zeroes of cubic polynomial x^3-2x^2+qx-r and alpha+beta=0, show that 2q=r.

Answer 1

Heya. !!!

here is the answer,

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Let α,β,γ be the zeros of the polynomial x^3−2x^2+qx−r 
such that α+β=0

Now, α+β+γ=
$- \frac{Coefficient \: of \: {x}^{2} }{Coefficient \: of \: {x}^{3} }$


⇒0+γ = − (−2/1) = 2

⇒γ=2

Since γ is a zero of the polynomial f(x). Therefore,    

 f(γ)=0

⇒γ^3−2γ^2+qγ−r = 0

⇒2^3−2(2^2)+2q−r = 0

⇒2q=r 

Regards


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Hope it helps u !!!

Cheers :))

# Nikky