Question

find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficient

${4s }^{2} - 4s + 1$
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Answer 1

Step-by-step explanation:

To find the zeros of the quadratic polynomial we consider

4s2 − 4s + 1 = 0

4s2 − 2s – 2s + 1 = 0

2s(2s – 1) -1(2s – 1) = 0

(2s – 1)(2s – 1) = 0

2s – 1 = 0 and 2s – 1 = 0

2s = 1 and 2s = 1

s = 1/2 and s = 1/2

∴ The zeroes of the polynomial = 1/2 and 1/2

Sum of the zeroes = -(coefficient of s)/(coefficient of s2)

Sum of the zeroes = -(-4)/4 = 1

Let’s find the sum of the roots = 1/2 + 1/2 = 1

Product of the zeros = Constant term / Coefficient of s2

Product of the zeros =1 / 4

Let’s find the products of the roots = 1/2 × 1/2 = 1/4

Answer 2

Step-by-step explanation:

Step-by-step explanation:

To find the zeros of the quadratic polynomial we consider

4s2 − 4s + 1 = 0

4s2 − 2s – 2s + 1 = 0

2s(2s – 1) -1(2s – 1) = 0

(2s – 1)(2s – 1) = 0

2s – 1 = 0 and 2s – 1 = 0

2s = 1 and 2s = 1

s = 1/2 and s = 1/2

∴ The zeroes of the polynomial = 1/2 and 1/2

Sum of the zeroes = -(coefficient of s)/(coefficient of s2)

Sum of the zeroes = -(-4)/4 = 1

Let’s find the sum of the roots = 1/2 + 1/2 = 1

Product of the zeros = Constant term / Coefficient of s2

Product of the zeros =1 / 4

Let’s find the products of the roots = 1/2 × 1/2 = 1/4