Question

If alpha and beta are the zeroes of quadratic polynomial f(x)=x2-2x+3 find a polynomial whose zeroes are (alpha+2) and(beta+2)

Answer 1

Sum of zeroes =alpha +beta=-b/a=2 (1)

product of zeroes=alpha ×beta=c/a=3 (2)

So the sum of zeroes of new polynomial is =alpha +beta+4 (Now from 1 and 2)

=2+4

=6

And the product of zeroes is =alpha×beta+2alpha+2beta +4

=alpha×beta+2(alpha × beta)+4

Now putting values from 1 and 2

=3+2(3)+4

=13

{x^2-(sum of zeroes)x+(product of zeroes)}

Putting the values we would get the new polynomial

X^2-6x+13 is the answer

I hope it helps u