Question

If α and β are the zeros of the quadratic polynomial x^2-x-2,then find the quadratic polynomial whose zeros are 2α+1 and 2β+1

Answer 1

x²-x-2
x²+x-2x-2
x(x+1)-2(x+1)
(x-2)(x+1)
α=2
β=-1
Zeroes of required equation = 2α+1, 2β+1
2α+1 = 2(2)+1
= 4+1
= 5
2β+1 = 2(-1)+1
= -2+1
= -1
Formula for making equation with desired roots = x²-(α+β)x + α.β
= x²-(-1+5)x+-1×5
= x²-(4)x-5
= x²-4x-5

Answer 2

Hey there !!!

P(x) = x²-x-2.
     
       =x²-2x+x-2

      =x(x-2)+1(x-2)

       (x+1)(x-2)=0

x+1=0 x-2=0

x=-1,2

α = -1 , β =2

2α+1=2*-1+1=-2+1=-1  2β+1 = 2*2+1 =5

So 2α+1 = -1 and 2β+1=5 are the roots of the new equation.

Q(x) = x²-(2α+1+2β+1)x+(2α+1)(2β+1)
        = x²-(5-1)x+5*-1
Q(x) =x²-4x-5

So Q(x) =x²-4x-5 is the equation whose roots are 2α+1 and 2β+1

Hope this helped you ............