Question

If α and β are the two zeros of the polynomial 21y square -y-2. Find the quadratic polynomial whose zeros are 2α and 2β

Answer 1

21y square-y-2

21y square-7y+6y-2=0

7y(3y-1)+2(3y-1)=0

3y-1=0,7y+2=0

y=1/3,-2/7

Let alpha =1/3 and betta =-2/7

2 alpha =1/3×2

2 betta =-2/7×2

polynomial =(x-2/3)(x+4/7)

=x square-26x/21-8/21

=21x square-26x-8