Question

12. If α and β are the zeroes of the quadratic polynomial x^2+2x+1, then find the quadratic polynomial whose zeroes are α^2β and αβ^2 .

class 10 maths chapter polynomials

Answer 1

Hello there
The given polynomial is x²+2x+1
To find its roots we have to factorise the equation.
x²+2x+1=0
or,x²+x+x+1=0
or,x(x+1)+(x+1)=0
or,(x+1)(x+1)=0
or,x=-1
So its both roots are equal to -1.
or,alpha=beta=-1
Now,
α²β =(-1)²(-1)=-1
and αβ² =(-1)(-1)²=-1
So the polynomial will be
(x-(-1))(x-(-1)
or,(x+1)(x+1)
or,x²+2x+1
Hence the polynomial is same as the original polynomial.
Hope it helps.