Question

If α and β are the zeroes of polynomial x2 - x - 6, find a polynomial whose zeros are 2α+2 and 2β+2.

Answer 1

We want roots to be $2\alpha+2 \: and\: 2\beta +2\\</p><p>\text{Put x as} \frac{x-2}{2}\\</p><p>\text{The quadratic now becomes:}\\</p><p>(\frac{x-2}{2})^2-(\frac{x-2}{2})-6=0\\</p><p>\implies (x-2)^2-2(x-2)-4 \times 6=0\\</p><p>\implies x^2-4x+4-2x+4-24=0\\</p><p>\implies x^2-6x-16=0$

Another method:

Steps:

1)Find original roots. They are:3 and -2.

2)Find new roots. 3(2)+2 and (-2)(2)+2 which are (8) and (-2)

3) Find the quadratic:

(x-8)(x+2)=0

x²-6x-16=0

Drawback of this method: Becomes difficult to use when the zeroes of the quadratic given are complex.

Answer 2

Answer:

very easy step to understand this question.