Question

If α and β are zeroes of polynomial 3x2+2x-6, then form a quadratic polynomial whose zeroes are 2α and 2β.

Answer 1

hope you will get it

Answer 2

Answer:

Step-by-step explanation:

The given quadratic polynomial is $3x^{2}+2x-6$, and if α, β are zeroes of polynomial, then

sum of zeroes(α+β) = $\frac{-b}{a}$ and product of zeroes(αβ)=$\frac{c}{a}$

(α+β)=$\frac{-2}{3}$ and (αβ)=$\frac{-6}{3}$

now, if zeroes of the new polynomial are 2α and 2β, then

2α+2β=2(α+β)=$2(\frac{-2}{3})=\frac{-4}{3}$

and 2(2αβ)=$4(\frac{-6}{3})=\frac{-24}{3}$

Therefore, the quadratic polynomial is: $x^{2}+\frac{4}{3}x-\frac{24}{3}$

=$3x^{2}+4x-24=0$