1.

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

Answer»

We WANT roots to be 2\alpha+2 \: and\: 2\beta +2\\\text{Put x as} \frac{x-2}{2}\\\text{The <klux>QUADRATIC</klux> now becomes:}\\(\frac{x-2}{2})^2-(\frac{x-2}{2})-6=0\\\implies (x-2)^2-2(x-2)-4 \times 6=0\\\implies x^2-4x+4-2x+4-24=0\\\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.


Discussion

No Comment Found

Related InterviewSolutions