Question

Find the zeroes of the following quadric polynomials and verify the relationship between The zeroes and the coefficients
1. x^2 - 2x - 8
2. 4s^2 - 4s + 1

Answer 1

4s²-4s+1

4s²-2s-2s+1

2s(2s-1)-1(2s-1)

(2s-1)(2s-1)

the two zeroes are

s=1/2,1/2

alpha +beta=-(coefficient of x)/(coefficient of x²)

=-(-4)/4

=1

alpha*beta= constant term/coefficient of x²

=1/4

is your answer

Answer 2

4s²-4s+1

4s²-2s-2s+1

2s(2s-1)-1(2s-1)

(2s-1)(2s-1)

the two zeroes are

s=1/2,1/2

alpha +beta=-(coefficient of x)/(coefficient of x²)

=-(-4)/4

=1

alpha*beta= constant term/coefficient of x²

=1/4

is your answer