Question

find the zeros of the quadratic polynomials and verify the relationship between the zeros and the coefficients. 1)4s^2-4s+1 2)4u^2+8u

Answer 1

(1) 4s² - 4s + 1 = 0
4s² -2s - 2s + 1 = 0
2s(2s-1) - 1(2s-1) = 0
(2s-1) (2s-1) = 0

s = ½,½ are zeroes of the polynomial

Relation between zeroes and coefficients,

Sum of zeroes = ½ + ½ = 1 = -x coefficient/x² coefficient
Product of zeroes = (½)(½) = ¼ = constant/x² coefficient

(2)4u² + 8u = 0
4u(u+2) = 0
u+2 = 0 ; u = -2
4u = 0 ; u = 0

-2 and 0 are zeroes of the given polynomial.

Relation between zeroes and coefficients :-

Sum of zeroes = -2 + 0 = -2 = -8/4 = -x coefficient/x² coefficient
Product of zeroes = (-2)(0) = 0 = constant/x² coefficient