Question

Find the zeros of the polynomial
p(s)=4s²-4s+1
and verify the

relationship between the zeros and coefficient. ​

Answer 1

Step-by-step explanation:

4s2 - 4s + 1 = 0

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

2s( 2s - 1 ) -1(2s - 1) = 0

(2s - 1) (2s - 1) = 0

2s - 1 = 0 2s - 1 = 0

2s = 1 2s = 1

s = 1/2 s = 1/2

Alpha = 1/2

Beta = 1/2

Sum of zeroes = Alpha + Beta

= 1/2 + 1/2

= 1

- Coefficient of x / Coefficient of x2 = -(-4)/4 = 1

Product of zeroes = Alpha × Beta

= 1/2 × 1/2

= 1/4

Constant / Coefficient of x2 = 1/4

Hence it is verified.

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